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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
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
field of group 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
Subnormal_subgroup
Group of languages related through a common ancestor
A language family is a group of languages related through descent from a common ancestor, called the proto-language of that family. The term family is
Language_family
Group that is also a differentiable manifold with group operations that are smooth
subgroup of G {\displaystyle G} admits a unique smooth structure which makes it an embedded Lie subgroup of G {\displaystyle G} —i.e. a Lie subgroup such
Lie_group
In mathematics, in the field of group theory, a subgroup H {\displaystyle H} of a group G {\displaystyle G} is termed malnormal if for any x {\displaystyle
Malnormal_subgroup
Every subgroup of a finite group is a contranormal subgroup of a subnormal subgroup. In general, every subgroup of a group is a contranormal subgroup of
Contranormal_subgroup
specifically group theory, an abnormal subgroup is a subgroup H of a group G such that for all x in G, x lies in the subgroup generated by H and H x, where H x
Abnormal_subgroup
theory, a quasinormal subgroup, or permutable subgroup, is a subgroup of a group that commutes (permutes) with every other subgroup with respect to the
Quasinormal_subgroup
Subgroup analysis refers to repeating the analysis of a study within subgroups of subjects defined by a subgrouping variable. For example: smoking status
Subgroup_analysis
Subgroup of phyllosilicate minerals within the kaolinite-serpentine group
Serpentine subgroup (part of the kaolinite-serpentine group in the category of phyllosilicates) are greenish, brownish, or spotted minerals commonly found
Serpentine_subgroup
Topics referred to by the same term
Parabolic subgroup may refer to: a parabolic subgroup of a reflection group a subgroup of an algebraic group that contains a Borel subgroup This disambiguation
Parabolic_subgroup
Smallest normal subgroup by which the quotient is commutative
commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. The commutator subgroup is important
Commutator_subgroup
Theorems that help decompose a finite group based on prime factors of its order
p} . A Sylow p-subgroup (sometimes p-Sylow subgroup) of a finite group G {\displaystyle G} is a maximal p {\displaystyle p} -subgroup of G {\displaystyle
Sylow_theorems
Special group in linear algebra
an Iwahori subgroup is a subgroup of a reductive algebraic group over a nonarchimedean local field that is analogous to a Borel subgroup of an algebraic
Iwahori_subgroup
Type of subgroup of an algebraic group
algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup. For example, in the general
Borel_subgroup
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
theory, a subgroup of a group is termed a special abelian subgroup or SA-subgroup if the centralizer of any nonidentity element in the subgroup is precisely
Special_abelian_subgroup
Concept in topology
compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups. Maximal
Maximal_compact_subgroup
Banana cultivar
fruits of one of a number of banana cultivars belonging to the Cavendish subgroup of the AAA banana cultivar group (triploid cultivars of Musa acuminata)
Cavendish_banana
mathematics, the Thompson subgroup J ( P ) {\displaystyle J(P)} of a finite p-group P refers to one of several characteristic subgroups of P. John G. Thompson (1964)
Thompson_subgroup
Very general problem in computer science
The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. It is a generalization of problems including
Hidden_subgroup_problem
Subgroup mapped to itself under every automorphism of the parent group
area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is mapped to itself by every automorphism of the parent group
Characteristic_subgroup
group theory, for a given group G, the diagonal subgroup of the n-fold direct product G n is the subgroup { ( g , … , g ) ∈ G n : g ∈ G } . {\displaystyle
Diagonal_subgroup
Matrix group
subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example is the subgroup of
Congruence_subgroup
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
groups over local fields, a hyperspecial subgroup of a reductive group G is a certain type of compact subgroup of G. In particular, let F be a nonarchimedean
Hyperspecial_subgroup
Mathematical theorem for algebraic structure of subgroups of free products
mathematical field of group theory, the Kurosh subgroup theorem describes the algebraic structure of subgroups of free products of groups. The theorem was
Kurosh_subgroup_theorem
Intersection of all maximal subgroups
group theory, the Frattini subgroup Φ ( G ) {\displaystyle \Phi (G)} of a group G is the intersection of all maximal subgroups of G. For the case that G
Frattini_subgroup
Topics referred to by the same term
A subgroup is an object in abstract algebra. Subgroup may also refer to: a subdivision of a group a subgroup of a galaxy group a taxonomic rank between
Subgroup_(disambiguation)
Lattice whose elements are the subgroups of a given group
In mathematics, the lattice of subgroups of a group G {\displaystyle G} is the lattice whose elements are the subgroups of G {\displaystyle G} , with the
Lattice_of_subgroups
In mathematics, in the field of group theory, a subgroup of a group is termed central if it lies inside the center of the group. Given a group G {\displaystyle
Central_subgroup
In mathematics, the Young subgroups of the symmetric group S n {\displaystyle S_{n}} are special subgroups that arise in combinatorics and representation
Young_subgroup
Theorem describing fusion of elements in Sylow subgroup of finite group
abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced
Focal_subgroup_theorem
Term in mathematics
the term maximal subgroup is used to mean slightly different things in different areas of algebra. In group theory, a maximal subgroup H of a group G is
Maximal_subgroup
Every subgroup of a cyclic group is cyclic, and if finite, its order divides its parent's
abstract algebra, every subgroup of a cyclic group is cyclic. Moreover, for a finite cyclic group of order n, every subgroup's order is a divisor of n
Subgroups_of_cyclic_groups
Sporadic simple group
The subgroups M23 and M22 then are easily defined to be the stabilizers of a single point and a pair of points respectively. M24 is the subgroup of S24
Mathieu_group_M24
of group theory, a conjugate-permutable subgroup is a subgroup that commutes with all its conjugate subgroups. The term was introduced by Tuval Foguel
Conjugate-permutable_subgroup
subgroup is a subgroup that is embedded in a nice way. Pronormality is a simultaneous generalization of both normal subgroups and abnormal subgroups such
Pronormal_subgroup
field of group theory, a subgroup A {\displaystyle A} of a group G {\displaystyle G} is termed seminormal if there is a subgroup B {\displaystyle B} such
Seminormal_subgroup
groups, a pure subgroup is a generalization of direct summand. It has found many uses in abelian group theory and related areas. A subgroup S {\displaystyle
Pure_subgroup
In algebraic topology, a peripheral subgroup for a space-subspace pair X ⊃ Y is a certain subgroup of the fundamental group of the complementary space
Peripheral_subgroup
mathematics, specifically group theory, a subgroup series of a group G {\displaystyle G} is a chain of subgroups: 1 = A 0 ≤ A 1 ≤ ⋯ ≤ A n = G {\displaystyle
Subgroup_series
Transformations induced by a mathematical group
finite-dimensional vector space, it allows one to identify many groups with subgroups of the general linear group GL ( n , K ) {\displaystyle \operatorname
Group_action
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
Mathematics group theory concept
In mathematics, specifically group theory, the index of a subgroup H in a group G is the number of left cosets of H in G, or equivalently, the number of
Index_of_a_subgroup
Group theory theorem
closed-subgroup theorem (sometimes referred to as Cartan's theorem) is a theorem in the theory of Lie groups. It states that if H is a closed subgroup of
Closed-subgroup_theorem
Type of group in abstract algebra
their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory. For the remainder
Symmetric_group
Formulary by the World Health Organization
Alternatives are 4th level ATC chemical subgroup (C09AA ACE inhibitors, plain) (for lisinopril) and 4th level ATC chemical subgroup (C08CA Dihydropyridine derivatives)
WHO Model List of Essential Medicines
WHO_Model_List_of_Essential_Medicines
Concept in mathematics
In mathematics, or more specifically group theory, the omega and agemo subgroups described the so-called "power structure" of a finite p-group. They were
Omega_and_agemo_subgroup
Any of certain special normal subgroups of a group
is any of certain 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
Core_(group_theory)
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
Restriction on topological groups in mathematics
said to have no small subgroup if there exists a neighborhood U {\displaystyle U} of the identity that contains no nontrivial subgroup of G . {\displaystyle
No_small_subgroup
Term used in transcendental number theory
In mathematics, the analytic subgroup theorem is a significant result in modern transcendental number theory. It may be seen as a generalisation of Baker's
Analytic_subgroup_theorem
In algebra, a nice subgroup H of an abelian p-group G is a subgroup such that pα(G/H) = 〈pαG,H〉/H for all ordinals α. Nice subgroups were introduced by
Nice_subgroup
Special types of subgroups encountered in group theory
S\subseteq G} fixed under conjugation. The centralizer and normalizer of S are subgroups of G. Many techniques in group theory are based on studying the centralizers
Centralizer_and_normalizer
The Han Chinese people can be defined into subgroups based on linguistic, cultural, ethnic, genetic, and regional features. The groups are termed minxi
Han_Chinese_subgroups
Group with subnormal series where all factors are abelian
solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof
Solvable_group
Maximal connected Abelian subgroup
In the theory of algebraic groups, a Cartan subgroup of a connected linear algebraic group G {\displaystyle G} over a (not necessarily algebraically closed)
Cartan_subgroup
In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. Let G {\displaystyle
Subgroup_growth
In abstract algebra, a basic subgroup is a subgroup of an abelian group which is a direct sum of cyclic subgroups and satisfies further technical conditions
Basic_subgroup
representation theory of algebraic groups, an observable subgroup is an algebraic subgroup of a linear algebraic group whose every finite-dimensional
Observable_subgroup
In cryptography, a subgroup confinement attack, or small subgroup confinement attack, on a cryptographic method that operates in a large finite group is
Small subgroup confinement attack
Small_subgroup_confinement_attack
Disjoint, equal-size subsets of a group's underlying set
In mathematics, specifically group theory, a subgroup H of a group G may be used to decompose the underlying set of G into disjoint, equal-size subsets
Coset
mathematical field of group theory, a subgroup H of a given group G is a serial subgroup of G if there is a chain C of subgroups of G extending from H to G such
Serial_subgroup
Abstract algebra concept
{\displaystyle \langle S\rangle } , the subgroup generated by S {\displaystyle S} , is the smallest subgroup of G {\displaystyle G} containing every element
Generating_set_of_a_group
Type of topological group
discrete if and only if its identity is isolated. A subgroup H of a topological group G is a discrete subgroup if H is discrete when endowed with the subspace
Discrete_group
List of cultivated varieties of banana
groups, cultivars may be divided into subgroups and then given a cultivar name, e.g. Musa AAA Group (Cavendish Subgroup) 'Robusta'. In practice, the scoring
List_of_banana_cultivars
Hierarchical level in biological classification
Zoologists sometimes use additional terms such as "species group", "species subgroup", "species complex" and "superspecies" for convenience as extra, but unofficial
Taxonomic_rank
Major subgroup of the Austronesian language family
being considered for merging. › The Malayo-Polynesian languages are a subgroup of the Austronesian languages, with approximately 385.5 million speakers
Malayo-Polynesian_languages
Mathematical group that can be generated as the set of powers of a single element
group G, one can form the subgroup that consists of all its integer powers: ⟨g⟩ = { gk | k ∈ Z }, called the cyclic subgroup generated by g. The order
Cyclic_group
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)
In mathematics, the Shimura subgroup Σ(N) is a subgroup of the Jacobian of the modular curve X0(N) of level N, given by the kernel of the natural map
Shimura_subgroup
mathematics, in the field of group theory, a paranormal subgroup is a subgroup such that the subgroup generated by it and any conjugate of it, is also generated
Paranormal_subgroup
Concept in geometric group theory
In geometric group theory, a discipline of mathematics, subgroup distortion measures the extent to which an overgroup can reduce the complexity of a group's
Subgroup_distortion
Geologic formation in the Hunter Region of Australia
Boolaroo Subgroup is a geologic formation in the Lachlan Orogen in eastern Australia in the Hunter Region. Formed in the late Permian, it is part of the
Boolaroo_Subgroup
In mathematics, the surface subgroup conjecture of Friedhelm Waldhausen states that the fundamental group of every closed, irreducible 3-manifold with
Surface_subgroup_conjecture
an area of abstract algebra, a strongly embedded subgroup of a finite group G is a proper subgroup H of even order such that H ∩ Hg has odd order whenever
Strongly_embedded_subgroup
Type of subgroup in group theory
field of group theory, a subgroup of a group is said to be ascendant if there is an ascending series starting from the subgroup and ending at the group
Ascendant_subgroup
taken to be a subgroup defined in terms of a prime number p, usually the local subgroups, the normalizers of the nontrivial p-subgroups. In which case
Local_property
subgroup H {\displaystyle H} of a finite group G {\displaystyle G} is said to be semipermutable if H {\displaystyle H} commutes with every subgroup K
Semipermutable_subgroup
Football league season
matches against teams from subgroup. Thus, before the second stage, new standings are formed in subgroup B. The teams in each subgroup will play in a single
2022–23_Russian_Second_League
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)
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
Operation in group theory
T are subgroups. The product of two subgroups S and T of a group G is itself a subgroup of G if and only if ST = TS. If S and T are subgroups of G, their
Product_of_group_subsets
Group that is a topological space with continuous group operations
H, which are open. 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
Topological_group
normal subgroup of the subgroup arises as the intersection with the subgroup of a normal subgroup of the whole group. In symbols, a subgroup H {\displaystyle
CEP_subgroup
Rock-forming minerals with predominantly silicate anions
Clinoptilolite subgroup – (Na,Ca,K)3−6(Al6−7Si29−30O72)·20H2O Erionite subgroup – (Na1−2,K1−2,Ca1−2)2Al4Si14O36·15H2O Faujasite subgroup – (Na1−2,Ca1−2
Silicate_mineral
Galaxies bound to the Milky Way
smaller galaxies gravitationally bound to it, as part of the Milky Way subgroup, which is part of the local galaxy cluster, the Local Group. There are
Satellite galaxies of the Milky Way
Satellite_galaxies_of_the_Milky_Way
Subgroup of the Algonquian languages
considered for merging. › The Eastern Algonquian languages constitute a subgroup of the Algonquian languages. Prior to European contact, Eastern Algonquian
Eastern_Algonquian_languages
subgroup is a subgroup that determines much of the structure of its containing group. The concept was generalized to essential submodules. A subgroup
Essential_subgroup
Concept in mathematics regarding sets operating on groups
g\in G.} A subgroup S of G is called a stable subgroup, Ω {\displaystyle \Omega } -subgroup or Ω {\displaystyle \Omega } -invariant subgroup if it respects
Group_with_operators
Group type in algebra
Z. A locally cyclic group is a group in which every finitely generated subgroup is cyclic. The free group on a finite set is finitely generated by the
Finitely_generated_group
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 G
Correspondence_theorem
Nilpotent, self-normalizing subgroup
of group theory, a Carter subgroup of a finite group G is a self-normalizing subgroup of G that is nilpotent. These subgroups were introduced by Roger
Carter_subgroup
Proposed branch of the Austronesian language family
the evidence for a Philippine subgroup as weak, and concludes that "they may represent more than one primary subgroup or perhaps an innovation-defined
Philippine_languages
Algebraic variety with a group structure
algebraic variety is an affine variety; they are exactly the algebraic subgroups of the general linear group, and are therefore also called linear algebraic
Algebraic_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
Theorem in group theory
algorithm and also for finding a presentation of a subgroup. Suppose H {\displaystyle H} is a subgroup of G {\displaystyle G} with generating set S {\displaystyle
Schreier's_lemma
Group of mathematical theorems
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 image
Isomorphism_theorems
SUBGROUP
SUBGROUP
SUBGROUP
SUBGROUP
Boy/Male
Muslim
Victories, Conquests
Boy/Male
Sikh
Gods light, Enlighted, Gods dear one (1)
Boy/Male
Hungarian
from the water'.
Girl/Female
Muslim
Boy/Male
Gujarati, Hindu, Indian, Tamil, Telugu
Lord of Truth; Truth
Boy/Male
Armenian
Name of a historian.
Boy/Male
British, Christian, English, German, Latin
Noble Friend; Intelligent; From Alba; A City on a White Hill
Girl/Female
German
Will-helmet. Famous Bearers: poet and playwright William Shakespeare (1564-1616) and William...
Boy/Male
Tamil
Hetvik | ஹேதà¯à®µà®¿à®•Â
Boy/Male
Greek Latin
King of Egypt; father of the Danaides.
SUBGROUP
SUBGROUP
SUBGROUP
SUBGROUP
SUBGROUP
n.
A subdivision of a group, as of animals.