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...

In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...

commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. The commutator subgroup is important...

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...

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...

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...

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...

In the theory of abelian groups, the torsion subgroup AT of an abelian group A is the subgroup of A consisting of all elements that have finite order...

{\displaystyle p} , a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G {\displaystyle G} is a maximal p {\displaystyle p} -subgroup of G {\displaystyle...

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...

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...

Subgroup analysis refers to repeating the analysis of a study within subgroups of subjects defined by a subgrouping variable. For example: smoking status...

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...

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...

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...

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...

their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory. For the remainder...

Serpentine subgroup (part of the kaolinite-serpentine group in the category of phyllosilicates) are greenish, brownish, or spotted minerals commonly found...

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...

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...

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...

solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof...

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...

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)...

finite-dimensional vector space, it allows one to identify many groups with subgroups of the general linear group GL(n, K), the group of the invertible matrices...

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...

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...

when talking about subgroups of G . {\displaystyle G.} The subgroups can thus be divided into conjugacy classes, with two subgroups belonging to the same...

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...

under multiplication. Every subgroup of an abelian group is normal, so each subgroup gives rise to a quotient group. Subgroups, quotients, and direct sums...