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Subgroup invariant under conjugation
In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation
Normal_subgroup
Subset of a group that forms a group itself
In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group
Subgroup
Mathematics group theory concept
{\displaystyle gHg^{-1}} of a subgroup H in G is equal to the index of the normalizer of H in G. If H is a subgroup of G, the index of the normal core of H satisfies
Index_of_a_subgroup
Type of group in abstract algebra
form a subgroup of index 2 in S, called the alternating subgroup A. Since A is even a characteristic subgroup of S, it is also a normal subgroup of the
Symmetric_group
Any of certain special normal subgroups of a group
special normal subgroups of a group. The two most common types are the normal core of a subgroup and the p-core of a group. For a group G, the normal core
Core_(group_theory)
Disjoint, equal-size subsets of a group's underlying set
elements of every subgroup H of G divides the number of elements of G. Cosets of a particular type of subgroup (a normal subgroup) can be used as the
Coset
Group obtained by aggregating similar elements of a larger group
element is always a normal subgroup of the original group, and the other equivalence classes are precisely the cosets of that normal subgroup. The resulting
Quotient_group
Operation in group theory
a subgroup H, and a normal subgroup N ◃ G {\displaystyle N\triangleleft G} , the following statements are equivalent: G is the product of subgroups, G
Semidirect_product
Smallest normal subgroup by which the quotient is commutative
important because it is the smallest normal subgroup such that the quotient group of the original group by this subgroup is abelian. In other words, G / N
Commutator_subgroup
Theorems that help decompose a finite group based on prime factors of its order
{\displaystyle p} . A Sylow p-subgroup of a group G {\displaystyle G} is a maximal p {\displaystyle p} -subgroup—that is, a p-subgroup of G {\displaystyle G}
Sylow_theorems
Property of a subgroup in mathematics
group theory, a subgroup of a group is said to be transitively normal in the group if every normal subgroup of the subgroup is also normal in the whole group
Transitively_normal_subgroup
Theorem in group theory
{\displaystyle N} is a normal subgroup of a group G {\displaystyle G} , then there exists a bijection from the set of all subgroups A {\displaystyle A} of
Correspondence_theorem
Group that is also a differentiable manifold with group operations that are smooth
connected normal solvable subgroup Gnil for the largest connected normal nilpotent subgroup so that we have a sequence of normal subgroups 1 ⊆ Gnil ⊆
Lie_group
Subgroup mapped to itself under every automorphism of the parent group
characteristic subgroup is normal; though the converse is not guaranteed. Examples of characteristic subgroups include the commutator subgroup and the center
Characteristic_subgroup
Smallest normal group containing a set
In group theory, the normal closure of a subset S {\displaystyle S} of a group G {\displaystyle G} is the smallest normal subgroup of G {\displaystyle
Normal_closure_(group_theory)
series (also normal series, normal tower, subinvariant series, or just series) of a group G is a sequence of subgroups, each a normal subgroup of the next
Subgroup_series
Term in mathematics
maximal subgroups, for example the Prüfer group. Similarly, a normal subgroup N of G is said to be a maximal normal subgroup (or maximal proper normal subgroup)
Maximal_subgroup
Group of mathematical theorems
kernel of f {\displaystyle f} is a normal subgroup of G {\displaystyle G} , The image of f {\displaystyle f} is a subgroup of H {\displaystyle H} , and The
Isomorphism_theorems
Mathematical concept
group G: G has a central series of finite length. That is, a series of normal subgroups { 1 } = G 0 ◃ G 1 ◃ ⋯ ◃ G n = G {\displaystyle \{1\}=G_{0}\triangleleft
Nilpotent_group
field of group theory, a subgroup H {\displaystyle H} of a group G {\displaystyle G} is called c-normal if there is a normal subgroup T {\displaystyle T} of
C-normal_subgroup
Theorem describing fusion of elements in Sylow subgroup of finite group
group has a normal subgroup of index p. The focal subgroup theorem relates several lines of investigation in finite group theory: normal subgroups of index
Focal_subgroup_theorem
Type of group in mathematics
connected components. The one that contains the identity element is a normal subgroup, called the special orthogonal group, and denoted SO(n). It consists
Orthogonal_group
Result pertaining to division rings
center of D, or K = D. In other words, if the unit group of K is a normal subgroup of the unit group of D, then either K = D or K is central (Lam 2001
Cartan–Brauer–Hua_theorem
Mathematics concept
(G)} is isomorphic to the kernel of φ {\displaystyle \varphi } , the normal subgroup of relations among the generators of G {\displaystyle G} . The extreme
Free_group
Commutative group (mathematics)
under multiplication. Every subgroup of an abelian group is normal, so each subgroup gives rise to a quotient group. Subgroups, quotients, and direct sums
Abelian_group
Set with associative invertible operation
is said to be a normal subgroup. In D 4 {\displaystyle \mathrm {D} _{4}} , the group of symmetries of a square, with its subgroup R {\displaystyle
Group_(mathematics)
Finite group
group theory, a branch of mathematics, a normal p-complement of a finite group for a prime p is a normal subgroup of order coprime to p and index a power
Normal_p-complement
Group that is a topological space with continuous group operations
If H is a subgroup of G, then the closure of H is also a subgroup. Likewise, if H is a normal subgroup of G, the closure of H is normal in G. If H is
Topological_group
Group with subnormal series where all factors are abelian
of the cyclic groups. Z 4 {\displaystyle \mathbb {Z} _{4}} is not a normal subgroup. A group G is called solvable if it has a subnormal series whose factor
Solvable_group
describes the relation between representations of a group and those of a normal subgroup. Alfred H. Clifford proved the following result on the restriction
Clifford_theory
Group of matrices with determinant 1
of ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the kernel of the determinant
Special_linear_group
Group for which a given group is a normal subgroup
is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q {\displaystyle Q} and N {\displaystyle N}
Group_extension
term in the series is a normal subgroup of its successor. The series may be infinite. If the series is finite, then the subgroup is subnormal. automorphism
Glossary_of_group_theory
Group of even permutations of a finite set
non-solvable group. The group A4 has the Klein four-group V as a proper normal subgroup, namely the identity and the double transpositions { (), (12)(34),
Alternating_group
Sporadic simple group
field F4 to number the rows: 0, 1, u, u2. The sextet group has a normal abelian subgroup H of order 64, isomorphic to the hexacode, a vector space of length
Mathieu_group_M24
Equivalence relation in algebra
the identity element is always a normal subgroup, and the other equivalence classes are the other cosets of this subgroup. Together, these equivalence classes
Congruence_relation
Group in which the order of every element is a power of p
contains normal subgroups of order pi with 0 ≤ i ≤ n, and any normal subgroup of order pi is contained in the ith center Zi. If a normal subgroup is not
P-group
Group without normal subgroups other than the trivial group and itself
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple
Simple_group
Concept in mathematics
element together with all elements not in any conjugate of H form a normal subgroup called the Frobenius kernel K. (This is a theorem due to Frobenius
Frobenius_group
Group of flat spacetime symmetries
group of spacetime translations is a normal subgroup, while the six-dimensional Lorentz group is also a subgroup, the stabilizer of the origin. The Poincaré
Poincaré_group
in the field of group theory, a subgroup H {\displaystyle H} of a group G {\displaystyle G} is said to be weakly normal if whenever H g ≤ N G ( H ) {\displaystyle
Weakly_normal_subgroup
Group of unitary complex matrices with determinant of 1
operation is matrix multiplication. The special unitary group is a normal subgroup of the unitary group U(n), consisting of all n × n unitary matrices
Special_unitary_group
If G is a finitely generated group with exponent n, is G necessarily finite?
two normal subgroups of finite index in any group is itself a normal subgroup of finite index. Thus, the intersection M of all the normal subgroups of
Burnside_problem
Group of symmetries of the square
of these normal subgroups, shown with a red background. In this table r means rotations, and f means flips. Because this subgroup is normal, the left
Dihedral_group_of_order_8
Type of topological group
Discrete normal subgroups play an important role in the theory of covering groups and locally isomorphic groups. A discrete normal subgroup of a connected
Discrete_group
Branch of mathematics that studies the properties of groups
the alternating group An is simple, i.e. does not admit any proper normal subgroups. This fact plays a key role in the impossibility of solving a general
Group_theory
Mathematical group whose commutator subgroup is abelian
group whose commutator subgroup is abelian. Equivalently, a group G is metabelian if and only if there is an abelian normal subgroup A such that the quotient
Metabelian_group
Group of symmetries of a regular polygon
four-group subgroups (which are normal in D4) has as normal subgroup order-2 subgroups generated by a reflection (flip) in D4, but these subgroups are not
Dihedral_group
Group without proper nontrivial characteristic subgroups
groups. A minimal normal subgroup of a group G is a nontrivial normal subgroup N of G such that the only proper subgroup of N that is normal in G is the trivial
Characteristically simple group
Characteristically_simple_group
complement of H, then H is a complement of K. Neither H nor K need be a normal subgroup of G. Complements need not exist, and if they do they need not be unique
Complement_(group_theory)
no nontrivial finite quotients. The quotient by the maximal proper normal subgroup is a finitely generated infinite simple group. Higman (1974) later
Higman_group
group theory, the Fitting subgroup F of a finite group G, named after Hans Fitting, is the unique largest normal nilpotent subgroup of G. Intuitively, it
Fitting_subgroup
a normal p-subgroup for some odd prime p, then Op′(G)Z(J(S)) is a normal subgroup of G, for any Sylow p-subgroup S. J(S) is the Thompson subgroup of
ZJ_theorem
Operation that combines groups
{\displaystyle G} and H {\displaystyle H} as subgroups, is generated by the elements of these subgroups, and is the “universal” group having these properties
Free_product
Groups of point isometries in 3 dimensions
a normal subgroup of O(2) and SO(2). Accordingly, in 3D, for every axis the cyclic group of k-fold rotations about that axis is a normal subgroup of
Point groups in three dimensions
Point_groups_in_three_dimensions
Elements taken to zero by a homomorphism
. ker f {\displaystyle \ker {f}} is a subgroup of G {\displaystyle G} and further it is a normal subgroup. Thus, there is a corresponding quotient
Kernel_(algebra)
Mathematical group that can be generated as the set of powers of a single element
group). Every finite subgroup of a cyclically ordered group is cyclic. A metacyclic group is a group containing a cyclic normal subgroup whose quotient is
Cyclic_group
follows: If M and N are nilpotent normal subgroups of a group G, then their product MN is also a nilpotent normal subgroup of G; if, moreover, M is nilpotent
Fitting's_theorem
Mathematical group
change the orientations of blocks. This group is a normal subgroup of G. It can be represented as the normal closure of some moves that flip a few edges or
Rubik's_Cube_group
the property of normality is transitive, that is, every subnormal subgroup is normal. Here are some facts about T-groups: Every simple group is a T-group
T-group_(mathematics)
Mathematical abelian group
3)(2,4), (1,4)(2,3)} In this representation, V {\displaystyle V} is a normal subgroup of the alternating group A 4 {\displaystyle A_{4}} (and also the symmetric
Klein_four-group
In group theory, equivalence class under the relation of conjugation
{\displaystyle S.} A normal subgroup is defined by the property that its conjugacy class contains a single member, namely itself. Normal subgroups play a key role
Conjugacy_class
Theorem in group theory
SD on Δ with minimal normal subgroup Tl. Moreover, N = Tkl is a minimal normal subgroup of G and G induces a transitive subgroup of Sk. PA (product action):
O'Nan–Scott_theorem
Isometry group of Euclidean space
x ↦ A x + c , {\displaystyle x\mapsto Ax+c,} with c = Ab T(n) is a normal subgroup of E(n): for every translation t and every isometry u, the composition
Euclidean_group
Topics referred to by the same term
a subgroup invariant under conjugation Normal (Ron "Bumblefoot" Thal album), 2005 Normal (Martin Mull album), 1974 "Normal" (Alonzo song) "Normal" (Eminem
Normal
Fundamental space of geometry
showing that it is a normal subgroup of the Euclidean group. The isometries that fix a given point P form the stabilizer subgroup of the Euclidean group
Euclidean_space
Intersection of all maximal subgroups
{\displaystyle \Phi (G)} is always a characteristic subgroup of G; in particular, it is always a normal subgroup of G. If G is finite, then Φ ( G ) {\displaystyle
Frattini_subgroup
Type of morphism
monomorphism f from H to G is normal if and only if its image is a normal subgroup of G. In particular, if H is a subgroup of G, then the inclusion map
Normal_morphism
Discrete subgroup in a locally compact topological group
group is a discrete subgroup with the property that the quotient space has finite invariant measure. In the special case of subgroups of Rn, this amounts
Lattice_(discrete_subgroup)
Non-abelian group of order eight
Q8 has three maximal normal subgroups: the cyclic subgroups generated by i, j, and k respectively. For each maximal normal subgroup N, we obtain a one-dimensional
Quaternion_group
Algebra describing 2D conformal symmetry
Algebraic structure → Group theory Group theory Basic notions Subgroup Normal subgroup Group action Quotient group (Semi-)direct product Direct sum Free
Virasoro_algebra
Transformations induced by a mathematical group
particular if H contains no nontrivial normal subgroups of G this induces an isomorphism from G to a subgroup of the permutation group of degree [G :
Group_action
Operation in group theory
or T is normal then the condition ST = TS is satisfied and the product is a subgroup. If both S and T are normal, then the product is normal as well.
Product_of_group_subsets
Monster and modular connection
quotient of the hyperbolic plane by subgroups of SL2(R), particularly, the normalizer Γ0(p)+ of the Hecke congruence subgroup Γ0(p) in SL(2,R). They found that
Monstrous_moonshine
Special types of subgroups encountered in group theory
′ ⊆ G {\displaystyle G'\subseteq G} where S {\displaystyle S} is a normal subgroup of G ′ {\displaystyle G'} . The definitions of centralizer and normalizer
Centralizer_and_normalizer
Theorem in group theory
{\displaystyle G} is a finite group, and N {\displaystyle N} is a normal subgroup whose order is coprime to the order of the quotient group G / N {\displaystyle
Schur–Zassenhaus_theorem
3D symmetry group
two normal subgroups, there is also a normal subgroup D2h (that of a cuboid), of type Dih2 × Z2 = Z2 × Z2 × Z2. It is the direct product of the normal subgroup
Tetrahedral_symmetry
In mathematics, specifically group theory, a Hall subgroup of a finite group G is a subgroup whose order is coprime to its index. They were introduced
Hall_subgroup
Index of articles associated with the same name
soc(G), is the subgroup generated by the minimal normal subgroups of G. It can happen that a group has no minimal non-trivial normal subgroup (that is, every
Socle_(mathematics)
Topic in group theory
Sylow 2-subgroup of S 4 {\displaystyle S_{4}} is the above C 2 ≀ C 2 {\displaystyle C_{2}\wr C_{2}} group. The Rubik's Cube group is a normal subgroup of index
Wreath_product
Mathematical concept
product of its subgroups G and H. In some contexts, the third property above is replaced by the following: 3′. Both G and H are normal in P. This property
Direct_product_of_groups
see ⊥. ⊲ ⊴ Normal subgroup of and normal subgroup of including equality, respectively. If N and G are groups such that N is a normal subgroup of (including
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
theory, a subgroup H of a given group G is a subnormal subgroup of G if there is a finite chain of subgroups of the group, each one normal in the next
Subnormal_subgroup
Lie group of Lorentz transformations
curve lying in the group. The restricted Lorentz group is a connected normal subgroup of the full Lorentz group with the same dimension, in this case with
Lorentz_group
Group of unitary matrices
\operatorname {U} (n)} is a 1 {\displaystyle 1} -dimensional abelian normal subgroup of U ( n ) {\displaystyle \operatorname {U} (n)} , the unitary group
Unitary_group
Second homology group of a group
presented in terms of a free group F on a set of generators, and a normal subgroup R generated by a set of relations on the generators, so that G ≅ F
Schur_multiplier
Orientation-preserving mapping class group of the torus
/N\mathbb {Z} )\to 1.} Being the kernel of a homomorphism Γ(N) is a normal subgroup of the modular group Γ. The group Γ(N) is given as the set of all modular
Modular_group
Subgroup of an abelian group consisting of all elements of finite order
of abelian groups, the torsion subgroup A T {\displaystyle A_{T}} of an abelian group A {\displaystyle A} is the subgroup of A {\displaystyle A} consisting
Torsion_subgroup
Algebraic variety with a group structure
subgroup is said to be normal if it is stable under every inner automorphism (which are regular maps). If H {\displaystyle \mathrm {H} } is a normal algebraic
Algebraic_group
Lattice whose elements are the subgroups of a given group
subnormal subgroups, and products of subnormal subgroups. For any Fitting class F, both the subnormal F-subgroups and the normal F-subgroups form lattices
Lattice_of_subgroups
Theorem on the orders of subgroups
mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is a divisor of |
Lagrange's theorem (group theory)
Lagrange's_theorem_(group_theory)
Mathematical group
smallest group 2G2(3) of type 2G2 is not simple, but it has a simple normal subgroup of index 3, isomorphic to A1(8). In the classification of finite simple
Group_of_Lie_type
Type of mathematical group
is a normal subgroup of finite index not containing that element. A group is residually finite if and only if the intersection of all its subgroups of finite
Residually_finite_group
Subgroup of the group of invertible n×n matrices
In mathematics, a linear algebraic group is a subgroup of the group of invertible n × n {\displaystyle n\times n} matrices (under matrix multiplication)
Linear_algebraic_group
the only nontrivial normal subgroups of 2O. The generalized quaternion group, Q16, also forms a subgroup of 2O, index 3. This subgroup is self-normalizing
Binary_octahedral_group
Extension of a cyclic group by a cyclic group
a metacyclic group is a group G {\displaystyle G} having a cyclic normal subgroup N {\displaystyle N} , such that the quotient G / N {\displaystyle G/N}
Metacyclic_group
Family of groups in mathematics
between "normal" (0) and "inverted" (1) (this combined operation is its own inverse). The subgroup of Dih(H) of elements (h, 0) is a normal subgroup of index
Generalized_dihedral_group
Sporadic simple group
2 elements. A large subgroup H (preferably a maximal subgroup) of the Monster is selected in which it is easy to perform calculations. The subgroup H chosen is
Monster_group
Theorem classifying finite simple groups
C/O(C) has a component (where O(C) is the core of C, the maximal normal subgroup of odd order). These are more or less the groups of Lie type of odd
Classification of finite simple groups
Classification_of_finite_simple_groups
Mathematical group based upon a finite number of elements
the classification of finite simple groups (those with no nontrivial normal subgroup) was completed in 2004. During the twentieth century, mathematicians
Finite_group
NORMAL SUBGROUP
NORMAL SUBGROUP
Boy/Male
French Teutonic American English German
From the north.
Biblical
treasurer of Nergal
Girl/Female
Indian
Soft
Male
Scottish
Scottish form of Irish Gaelic Cormac, CORMAG means "son of defilement."
Boy/Male
Biblical
Treasurer of Nergal.
Girl/Female
Indian, Punjabi, Sikh, Telugu
Pure; Without Any Impurity
Boy/Male
Scottish American
From the north valley.
Girl/Female
Latin American
Rule; pattern. Can also be a feminine form of Norman: from the North.
Boy/Male
Assamese, Bengali, Celebrity, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Punjabi, Sikh, Sindhi, Tamil, Telugu, Traditional
Kindness; Clean; Pure; Talent Person; The One who is Pure
Girl/Female
American, Australian, British, Chinese, Christian, Danish, English, Finnish, French, German, Latin, Swedish
From the North; Pattern; Courage; Norseman; Rule; Standard; Female Version of Norman
Boy/Male
Shakespearean
Hamlet, Prince of Denmark' Fortinbras, Prince of Norway.
Surname or Lastname
English, Irish (Ulster), Scottish, and Dutch
English, Irish (Ulster), Scottish, and Dutch : name applied either to a Scandinavian or to someone from Normandy in northern France. The Scandinavian adventurers of the Dark Ages called themselves norðmenn ‘men from the North’. Before 1066, Scandinavian settlers in England were already fairly readily absorbed, and Northman and Normann came to be used as bynames and later as personal names, even among the Saxon inhabitants. The term gained a new use from 1066 onwards, when England was settled by invaders from Normandy, who were likewise of Scandinavian origin but by now largely integrated with the native population and speaking a Romance language, retaining only their original Germanic name.French : regional name for someone from Normandy.Dutch : ethnic name for a Norwegian.Jewish (Ashkenazic) : variant of Nordman.Jewish : Americanized form of some like-sounding Ashkenazic name.Swedish : from norr ‘north’ + man ‘man’.Albert Andriessen Bradt, a settler in Rensselaerswijck on the upper Hudson River in NY, was originally from Norway and was known as de Norrman (‘the Norwegian’). The waterway south of Albany which powered his mills became known as the Normanskill (‘the Norman’s Waterway’), by which name it is still known today.
Boy/Male
American, Australian, French, Scottish
From the Northern Town
Boy/Male
Afghan, Arabic
Handsome
Male
English
English form of Norwegian Normund, NORMAND means "north protection."
Boy/Male
Hindu
Clean, Pure
Female
Italian
 Italian name invented by Felice Romani in his libretto for Belini's opera of the same name, derived from Latin norma, NORMA means "standard, rule." Compare with another form of Norma.
Male
English
English form of Teutonic Nordemann, NORMAN means "northman."
Female
English
English name derived from the gem name, from Latin corallium, probably ultimately from Hebrew goral, CORAL means "small pebble."
Female
English
 Feminine form of English Norman, NORMA means "northman." Compare with another form of Norma.
NORMAL SUBGROUP
NORMAL SUBGROUP
Boy/Male
Indian, Kannada
God of Starts
Male
Greek
(Δαίμων) Ancient Greek name derived from the word demos, DEMON means "the people."
Girl/Female
Arabic, Muslim
Assembly
Boy/Male
Sikh
One imbued by the blissful soul
Girl/Female
Afghan, Arabic, Hebrew, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Sindhi, Tamil
Pleased; Happy; Encampment; Resting Place
Female
English
Variant spelling of English Trudy, TRUDI means "spear strength."
Boy/Male
Hindu, Indian
Flowery
Boy/Male
Scottish
Great cheif, world mighty. From the Gaelic Domhnall. The name Donald has been borne by a number...
Surname or Lastname
English and Jewish (Ashkenazic)
English and Jewish (Ashkenazic) : habitational name for someone who came from London or a nickname for someone who had made a trip to London or had some other connection with the city. In some cases, however, the Jewish name was purely ornamental. The place name, recorded by the Roman historian Tacitus in the Latinized form Londinium, is obscure in origin and meaning, but may be derived from pre-Celtic (Old European) roots with a meaning something like ‘place at the navigable or unfordable river’.
Boy/Male
Norse Scottish
Dwells at the village.
NORMAL SUBGROUP
NORMAL SUBGROUP
NORMAL SUBGROUP
NORMAL SUBGROUP
NORMAL SUBGROUP
a.
Alt. of Loral
a.
Done in due form, or with solemnity; according to regular method; not incidental, sudden or irregular; express; as, he gave his formal consent.
n.
The quality, state, or fact of being normal; as, the point of normalcy.
a.
Northern; pertaining to the north, or to the north wind; as, a boreal bird; a boreal blast.
a.
Serving to teach or convey a moral; as, a moral lesson; moral tales.
adv.
In a normal manner.
n.
See Mormal.
a.
According to a square or rule; perpendicular; forming a right angle. Specifically: Of or pertaining to a normal.
a.
According to an established norm, rule, or principle; conformed to a type, standard, or regular form; performing the proper functions; not abnormal; regular; natural; analogical.
a.
Pertaining to, or situated near, the back, or dorsum, of an animal or of one of its parts; notal; tergal; neural; as, the dorsal fin of a fish; the dorsal artery of the tongue; -- opposed to ventral.
a.
Sound; normal.
a.
Human; belonging to man, who is mortal; as, mortal wit or knowledge; mortal power.
a.
Denoting that series of hydrocarbons in which no carbon atom is united with more than two other carbon atoms; as, normal pentane, hexane, etc. Cf. Iso-.
a.
Having the form or appearance without the substance or essence; external; as, formal duty; formal worship; formal courtesy, etc.
a.
Of or pertaining to Normandy or to the Normans; as, the Norman language; the Norman conquest.
n.
See Wormil.
a.
Denoting certain hypothetical compounds, as acids from which the real acids are obtained by dehydration; thus, normal sulphuric acid and normal nitric acid are respectively S(OH)6, and N(OH)5.
a.
Both renal and portal. See Portal.
n.
See Wormil.
a.
Not according to rule; abnormal.