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Finite group
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 of p. In other words
Normal_p-complement
Tool in linear algebra and matrix analysis
so that M is a (p + q) × (p + q) matrix. If D is invertible, then the Schur complement of the block D of the matrix M is the p × p matrix defined by
Schur_complement
Any of certain special normal subgroups of a group
every p-soluble group is p-constrained. A group is p-nilpotent if and only if it has a normal p-complement, which is just its p′-core. Just as normal cores
Core_(group_theory)
as the exponent of p increases. Most groups of small order have a Sylow p subgroup P with a normal p-complement N for some prime p dividing the order
List_of_small_groups
symmetrical: if K is a 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
Complement_(group_theory)
Concept in mathematics
X is called a Frobenius complement. The identity element together with all elements not in any conjugate of H form a normal subgroup called the Frobenius
Frobenius_group
Binary representation for signed numbers
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point
Two's_complement
Automorphism group of the Klein quartic
its Sylow 2-subgroup provide a counter-example for various normal p-complement theorems for p = 2. G = PSL(2, 7) acts via linear fractional transformation
PSL(2,7)
German mathematician (1849–1917)
145–146. ISBN 0-8218-1967-4. Theorem 9.4.1., p. 145, at Google Books Thompson, J.G. (1959). "Normal p-complements for finite groups". Mathematische Zeitschrift
Ferdinand_Georg_Frobenius
Probability distribution
\left({\frac {a-\mu }{\sigma {\sqrt {2}}}}\right)\right]} The complement of the standard normal cumulative distribution function, Q ( x ) = 1 − Φ ( x ) {\textstyle
Normal_distribution
English mathematician
representations, where he helped to develop some of the foundational theory, complementing, and sometimes competing with, the work of Ferdinand Georg Frobenius
William_Burnside
Part of the immune system that enhances the ability of antibodies and phagocytic cells
The complement system, also known as complement cascade, is a part of the humoral, innate immune system and enhances (complements) the ability of antibodies
Complement_system
Method of subtraction
In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they
Method_of_complements
Thompson subgroup and denoted by J ( P ) {\displaystyle J(P)} . Glauberman normal p-complement theorem ZJ theorem Puig subgroup, a subgroup analogous to
Thompson_subgroup
Graph with same nodes as but complementary connections to another
graph and let P consist of all pairs of distinct vertices in V. Then the simple undirected graph H = (V, P \ E) is the complement of G, where P \ E is the
Complement_graph
American mathematician (born 1941)
University Press, ISBN 978-0-521-45716-3, MR 1311244 Glauberman normal p-complement theorem Curriculum vitae, retrieved 2013-07-21. George Glauberman
George_Glauberman
Bound lattice in which every element has a complement
theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element
Complemented_lattice
(on a complex Hilbert space) continuous linear operator
Eigenvectors of a normal operator corresponding to different eigenvalues are orthogonal, and a normal operator stabilizes the orthogonal complement of each of
Normal_operator
Medical condition
Complement deficiency is an immunodeficiency of absent or suboptimal functioning of one of the complement system proteins. Because of redundancies in
Complement_deficiency
Logical operation
logical complement, is an operation that takes a proposition P {\displaystyle P} to another proposition "not P {\displaystyle P} ", written ¬ P {\displaystyle
Negation
Theorem in group theory
of the theorem is that any normal Hall subgroup N {\displaystyle N} of a finite group G {\displaystyle G} has a complement in G {\displaystyle G} . Moreover
Schur–Zassenhaus_theorem
Standard forms of Boolean functions
be expressed in the canonical disjunctive normal form (CDNF), minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms
Canonical_normal_form
Broadway musical
production numbers" had been replaced by songs that complemented the emotional content of the book. Next to Normal began previews on Broadway at the Booth Theatre
Next_to_Normal
Generalization of the one-dimensional normal distribution to higher dimensions
normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution
Multivariate normal distribution
Multivariate_normal_distribution
Pathological embedding of the sphere in 3D space
necklace, a Cantor set in R 3 {\displaystyle \mathbb {R} ^{3}} whose complement is not simply connected. Antoine's construction used a sequence of interlocking
Alexander_horned_sphere
{\displaystyle \complement _{A}B=A\setminus B} . 2. Without a subscript, denotes the absolute complement; that is, ∁ A = ∁ U A {\displaystyle \complement A=\complement
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Probability distribution
calculated by its complement as f ( k , n , p ) = f ( n − k , n , 1 − p ) . {\displaystyle f(k,n,p)=f(n-k,n,1-p).} Looking at the expression f(k, n, p) as a function
Binomial_distribution
Protein-coding gene in the species Homo sapiens
encoded by the CFP (complement factor properdin) gene. Properdin and factor H are regulatory proteins in the alternative complement pathway. Properdin
Properdin
Typographical symbol (™)
preceding mark is a trademark, specifically an unregistered trademark. It complements the registered trademark symbol ® which is reserved for trademarks registered
Trademark_symbol
Opposite of a probability event
probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur. The event A and its complement [not A] are mutually
Complementary_event
Number with all digits equally frequent
the complement of X has measure 0. If x is normal in base b, and a ≠ 0 is a rational number, then x ⋅ a {\displaystyle x\cdot a} is also normal in base
Normal_number
Protein found in humans
Complement receptor type 1 (CR1) also known as C3b/C4b receptor or CD35 (cluster of differentiation 35) is a protein that in humans is encoded by the CR1
Complement_receptor_1
American WWII-era fighter aircraft
Designer, Edgar Schmued and the P-51, p. 61. The comparison was between wind-tunnel tests of full-scale models, with normal heating (thermic engine) and
North_American_P-51_Mustang
Protein found in humans
Complement receptor type 2 (CR2), also known as complement C3d receptor, Epstein–Barr virus receptor, and CD21 (cluster of differentiation 21), is a protein
Complement_receptor_2
Maritime patrol and anti-submarine aircraft family
the type. In U.S. Navy service, the normal crew complement was 12 until it was reduced to its current complement of 11 in the early 2000s when the in-flight
Lockheed_P-3_Orion
Immunity strategy in living beings
chemical factors, including chemical mediators called cytokines activate the complement cascade to identify bacteria, activate cells, and promote clearance of
Innate_immune_system
Dietary theory for protein nutrition
Protein combining or protein complementing is a dietary theory for protein nutrition that purports to optimize the biological value of protein intake
Protein_combining
Generalization of perpendicularity
{\displaystyle V} that is orthogonal to a given subspace is its orthogonal complement. Given a module M {\displaystyle M} and its dual M ∗ {\displaystyle M^{*}}
Orthogonality_(mathematics)
Number of sets of chromosomes of a cell
chromosomes within each of the 23 homologous pairs, providing a full complement of 46 chromosomes. This total number of individual chromosomes (counting
Ploidy
Boolean polynomials as sums of monomials
Algebraic normal form (ANF) is a representation of functions in boolean algebra. Formulas written in ANF are also known as ring sum normal form (RSNF or
Algebraic_normal_form
Angle in geometric optics
tangent, rather than that between the beam and the surface normal. The 90-degree complement to the angle of incidence is called the grazing angle or glancing
Angle_of_incidence_(optics)
Reduced oxygen-carrying ability of the blood due to breakdown of red blood cells
acquired, potentially life-threatening disease of the blood characterized by complement-induced intravascular hemolytic anemia. Lead poisoning resulting from
Hemolytic_anemia
Shorthand used in statistics
68–95–99.7 rule, also known as the empirical rule or 68–95–99.7 rule for a normal distribution and sometimes abbreviated 3sr or 3 σ, is a shorthand used to
68–95–99.7_rule
Mammalian protein found in humans
or dying cells (and some types of bacteria) in order to activate the complement system via C1q. CRP is synthesized by the liver in response to factors
C-reactive_protein
Function of the observed sample results
hypothesis tests and p-values, and their connection to replicability. It states that "Different measures of uncertainty can complement one another; no single
P-value
Presence of an abnormal number of chromosomes in a cell
attached to both mitotic spindle poles. One daughter cell would have a normal complement of chromosomes; the second would lack one. A third daughter cell may
Aneuploidy
Pair of logical equivalences
"not A and not B". or The complement of the union of two sets is the same as the intersection of their complements The complement of the intersection of
De_Morgan's_laws
Concept in mathematics
submanifold. Define, for a given p ∈ S {\displaystyle p\in S} , a vector n ∈ T p M {\displaystyle n\in \mathrm {T} _{p}M} to be normal to S {\displaystyle S} whenever
Normal_bundle
Part of the innate immune system
C3b is the larger of two elements formed by the cleavage of complement component 3, and is considered an important part of the innate immune system. C3b
C3b
closed set C and any point p in its complement there exists a cover in the collection such that every neighbourhood of p in the cover is disjoint from
Moore_space_(topology)
Number measuring the chance an event occurs
{\displaystyle {\overline {A}},A^{\complement },\neg A} , or ∼ A {\displaystyle {\sim }A} ; its probability is given by P(not A) = 1 − P(A). As an example, the chance
Probability
Immune organ that filters blood
bacteria. Encapsulated bacteria inhibit the binding of complement or prevent the complement assembled on the capsule from interacting with macrophage
Spleen
British battlecruiser, 1916–1939
Britain and Ireland. She briefly became a training ship, but reverted to her normal role a few months before the start of the Second World War in September
HMS_Courageous_(50)
Class of enzymes
proactivator convertase, properdin factor D esterase, factor D (complement), complement factor D, CFD, adipsin) is a protein which in humans is encoded
Factor_D
Genetic disease causing anemia, birth defects, and cancers
Fanconi anemia has improved scientific understanding of the mechanisms of normal bone marrow function and the development of cancer. Among those affected
Fanconi_anemia
Set whose pairs have minima and maxima
bounded lattice for which every element has a complement is called a complemented lattice. A complemented lattice that is also distributive is a Boolean
Lattice_(order)
WP 512 Friedman. British Destroyers. p. 311. The Navy List. (July 1931). p. 268. The Navy List. (July 1937). p. 273 Mason, Geoffrey B. "HMS Scimitar
HMS_Scimitar_(H21)
Complement control proteins are proteins that interact with components of the complement system. The complement system is tightly regulated by a network
Complement_control_protein
American mathematician (1946–2012)
figure-eight knot complement. By utilizing Haken's normal surface techniques, he classified the incompressible surfaces in the knot complement. Together with
William_Thurston
Medical condition
instigates activation of the entire complement pathway. Consequently, levels of all complement proteins become low. The complement pathway is composed of several
Urticarial_vasculitis
Autoimmune disease in which the immune system attacks healthy tissue
RNASEH2C, Complement component 1qA, Complement component 1qB, Complement component 1r, Complement component 1s, Complement component 2, Complement component
Lupus
Historically Black university in Hampton, Virginia, US
girls and Black boys. Hampton Normal and Agricultural Institute became simply Hampton Institute in 1930. In 1931 the George P. Phenix School for all age
Hampton_University
In mathematical logic, an atomic formula or its negation
In the context of a formula in the conjunctive normal form, a literal is pure if the literal's complement does not appear in the formula. In Boolean functions
Literal_(mathematical_logic)
Country in North America
Buchwald, M. (1992). "Cloning of cDNAs for Fanconi's anemia by functional complementation". Nature. 356 (6372): 763–767. doi:10.1038/356763a0. PMID 1574115.
Canada
Decreased ability to see color or color differences
exist. The below table shows the cone complements for different types of human color vision. The cone complement contains the types of cones (or their
Color_blindness
Royal Navy S class destroyer
training-only director, single Dumaresq and a Vickers range clock. The ship had a complement of 90 officers and ratings. Laid down on 10 September 1917 during the
HMS_Saladin
Concept in probability theory
distribution, conjugate prior of the covariance matrix of a multivariate normal distribution, for an example where a large dimensionality is involved.)
Conjugate_prior
Disease characterized by rapid swelling
angioedema, bradykinin formation is caused by continuous activation of the complement system due to a deficiency in one of its prime inhibitors, C1-esterase
Angioedema
Logical connective AND
for true (1) and false (0), then logical conjunction works exactly like normal arithmetic multiplication. In high-level computer programming and digital
Logical_conjunction
fire at 08:55 when Hoel rolled over and sank. Only eight-six of Hoel's complement survived; two hundred and fifty three officers and crew died with their
List of U.S. Navy ships sunk or damaged in action during World War II
List_of_U.S._Navy_ships_sunk_or_damaged_in_action_during_World_War_II
S class destroyer in WW II
miles (5,090 km; 3,160 mi) at 15 knots (28 km/h; 17 mph). The ship had a complement of 90 officers and ratings. Armament consisted of three QF 4-inch (102 mm)
HMS_Stronghold
Multi-ship class of aircraft carrier
and the ships had a complete double bottom. In 1939, Courageous had a complement of 807 officers and ratings, plus 403 men in her air group. Their half-sister
Courageous-class aircraft carrier
Courageous-class_aircraft_carrier
Autoimmune disease resulting in skeletal muscle weakness
IgG3 antibodies that attack AChR in the postsynaptic membrane, causing complement-mediated damage and muscle weakness. Rarely, an inherited genetic defect
Myasthenia_gravis
Vision loss due to damage to the macula of the eye
Haines JL, Hauser MA, Schmidt S, Scott WK, Olson LM, Gallins P, et al. (April 2005). "Complement factor H variant increases the risk of age-related macular
Macular_degeneration
English football club season
of red and white. The shirt has a red body and white sleeves, and is complemented by white shorts and white socks. Red socks were used in some away games
2023–24_Arsenal_F.C._season
On solvability of Diophantine equations
equations p 1 = 0 , … , p k = 0 {\displaystyle p_{1}=0,\ldots ,p_{k}=0} (where each p i {\displaystyle p_{i}} is a polynomial) as a single equation p 1 2 +
Hilbert's_tenth_problem
two players to the same defensive position during a season, normally to complement a batter who hits well against left-handed pitchers with one who hits
Glossary_of_baseball_terms
any two Sylow systems are conjugate. Any normal Hall subgroup H of a finite group G possesses a complement, that is, there is some subgroup K of G that
Hall_subgroup
Function returning one of only two values
every argument or complement (minterms) Full (canonical) conjunctive normal form, an AND of ORs each containing every argument or complement (maxterms) Blake
Boolean_function
Professional basketball tournament
Heat. Tatum's performance of 23 points, 10 rebounds, and 10 assists was complemented by his teammates, as they knocked down 21 of Boston's 22 three-pointers
2024_NBA_playoffs
synthesized by RNA polymerase, which builds a chain of ribonucleotides that complement the deoxyribonucleotides of a DNA template; in this way, the DNA sequence
Glossary of cellular and molecular biology (M–Z)
Glossary_of_cellular_and_molecular_biology_(M–Z)
Curve generated by the projections of a fixed point on the tangents of another curve
fixed point P, as the variable point R ranges over the curve C. Complementing the pedal curve, there is a unique point Y on the line normal to C at R so
Pedal_curve
Destroyer of the Royal Navy
establishment at Plymouth, but did not stay long and was reduced to Reduced Complement on 5 March 1919. The Royal Navy was rationalising its destroyer force
HMS_Sharpshooter_(1917)
Genetic condition in which a male has an extra Y chromosome
risk of learning disabilities. Most individuals with this condition have normal fertility. The condition is generally not inherited but rather occurs as
XYY_syndrome
British M-Class destroyer
also fitted with racks and storage for depth charges. The ship had a complement of 80 officers and ratings. Prince was laid down by Alexander Stephens
HMS_Prince_(1916)
Disorder resulting in severe swelling
now called HAE with normal C1 inhibitor (HAE-nl-C1INH). Types I and II affect females and males equally, while HAE with normal C1 inhibitor affects females
Hereditary_angioedema
British navy ships
miles (3,440 km; 2,140 mi) at 20 knots (37 km/h; 23 mph). They had a complement of 82 officers and ratings. The ships had a main armament consisting of
Yarrow Later M-class destroyer
Yarrow_Later_M-class_destroyer
Biological system protecting an organism against disease
phagocytosis, antimicrobial peptides called defensins, RNA interference, and the complement system. Jawed vertebrates, including humans, have a more sophisticated
Immune_system
British M-Class destroyer
consisted of two twin mounts for 21 in (533 mm) torpedoes. The ship had a complement of 76 officers and ratings. Onslaught was launched by Fairfield Shipbuilding
HMS_Onslaught_(1915)
IEEE standard for floating-point arithmetic
the exponent regardless of precision. CDC and Cray computers used ones' complement representation, which admits a value of +0 and −0. CDC 60-bit computers
IEEE_754
Group of genetic connective tissues disorders
are those that affect glycosaminoglycan biosynthesis. Defects in the complement pathway characterize Group E disorders. Group F are disorders of intracellular
Ehlers–Danlos_syndrome
Number in {..., –2, –1, 0, 1, 2, ...}
practical computers are of finite capacity. Also, in the common two's complement representation, the inherent definition of sign distinguishes between
Integer
Subgroup of a group in mathematics
retracts: A subgroup is a retract if and only if it has a normal complement. The normal complement, specifically, is the kernel of the retraction. Every direct
Retract_(group_theory)
Portuguese football manager (born 1963)
advice and analyses of the opposition. Robson and Mourinho's styles complemented each other: the Englishman favoured an attacking style, while Mourinho
José_Mourinho
Avionics data bus standard
sign, the SSM is also considered to be indicating Normal Operation. In the case of two's-complement representation of signed binary numbers (BNR), Bit
ARINC_429
Commutative group (mathematics)
abelian group G {\displaystyle G} then A {\displaystyle A} admits a direct complement: a subgroup C {\displaystyle C} of G {\displaystyle G} such that G = A
Abelian_group
Chicago "L" station
featuring large amounts of steel and glass and very little amenities, to complement the design of the brand new stainless-steel 2200 series trains that ran
69th_station
Data structure for Boolean functions
compactly, using complemented edges, also known as complement links. The resulting BDD is sometimes known as a typed BDD or signed BDD. Complemented edges are
Binary_decision_diagram
Countable intersection of open sets
sets { q } c {\displaystyle \{q\}^{c}} (the superscript denoting the complement) where q {\displaystyle q} is rational. The set of rational numbers Q
Gδ_set
2024 studio album by Taylor Swift
monotonous and "staid", but others argued that the minimalistic approach complemented Swift's hyper-personal lyrics; Hopper opined that "Swift's confidence
The_Tortured_Poets_Department
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
Male
Hungarian
Hungarian form of English Philip, FÜLÖP means "lover of horses."
Biblical
treasurer of Nergal
Male
English
English form of Teutonic Nordemann, NORMAN means "northman."
Boy/Male
French Teutonic American English German
From the north.
Boy/Male
Hindu
Clean, Pure
Boy/Male
Scottish American
From the north valley.
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
Male
English
English form of Norwegian Normund, NORMAND means "north protection."
Female
English
 Feminine form of English Norman, NORMA means "northman." Compare with another form of Norma.
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
Biblical
Treasurer of Nergal.
Boy/Male
Shakespearean
Hamlet, Prince of Denmark' Fortinbras, Prince of Norway.
Girl/Female
Indian
Soft
Boy/Male
Afghan, Arabic
Handsome
Male
Scottish
Scottish form of Irish Gaelic Cormac, CORMAG means "son of defilement."
Female
English
English name derived from the gem name, from Latin corallium, probably ultimately from Hebrew goral, CORAL means "small pebble."
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.
Girl/Female
Latin American
Rule; pattern. Can also be a feminine form of Norman: from the North.
Girl/Female
Indian, Punjabi, Sikh, Telugu
Pure; Without Any Impurity
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
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
Girl/Female
Arabic
Beautiful
Boy/Male
Australian, British, English, Hebrew
Right-hand Son; Similar to Benedict; Son of the Right Hand
Boy/Male
Indian, Sanskrit
Possessor of the Cakra; Worshipper of Vishnu
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : topographic name for someone who lived by land on which beans were grown, from Old English bēan + land.
Girl/Female
Australian, Czech, Danish, German
Peace
Boy/Male
Biblical
Peaceable, perfect, that rewards.
Surname or Lastname
English and Irish
English and Irish : variant of Neville.
Girl/Female
Muslim
The light of happiness
Girl/Female
Hindu, Indian
Daughter of a Cow Herd
Boy/Male
Tamil
A name of Lord Buddha
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
a.
Both renal and portal. See Portal.
a.
According to a square or rule; perpendicular; forming a right angle. Specifically: Of or pertaining to a normal.
n.
See Mormal.
a.
Sound; normal.
a.
Not according to rule; abnormal.
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.
Serving to teach or convey a moral; as, a moral lesson; moral tales.
a.
Human; belonging to man, who is mortal; as, mortal wit or knowledge; mortal power.
n.
See Wormil.
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.
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.
Having the form or appearance without the substance or essence; external; as, formal duty; formal worship; formal courtesy, etc.
a.
Alt. of Loral
adv.
In a normal manner.
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.
Of or pertaining to Normandy or to the Normans; as, the Norman language; the Norman conquest.
a.
Northern; pertaining to the north, or to the north wind; as, a boreal bird; a boreal blast.
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-.