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...

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

a composition series is a maximal subnormal series, while a chief series is a maximal normal series. If a group G has a normal subgroup N, then the factor...

the fields of group theory and Lie theory, a central series is a kind of normal series of subgroups or Lie subalgebras, expressing the idea that the commutator...

Theory. Krieger, 1975. Schmidt, Roland. Subgroup Lattices of Groups. de Gruyter, 1994. Keith Conrad, SUBGROUP SERIES II, Section 4 , http://www.math.uconn...

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

normal subgroup of G/Ni. Equivalently, there does not exist any subgroup A normal in G such that Ni < A < Ni+1 for any i. In other words, a chief series may...

investigations of nilpotent normal subgroups. A Fitting chain (or Fitting series or nilpotent series) for a group is a subnormal series with nilpotent quotients...

for any pair g, h ∈ G. ascendant subgroup A subgroup H of a group G is ascendant if there is an ascending subgroup series starting from H and ending at G...

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

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...

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...

{\displaystyle j\geq 1} , of the lower central series of a pro-p group S {\displaystyle S} are closed (and open) subgroups of finite index, and therefore the corresponding...

2016. Retrieved January 30, 2017. "John Glenn Archives, Audiovisuals Subgroup, Series 3: Certificates". Ohio State University. Archived from the original...

years, as Amish churches have divided many times over doctrinal disputes, subgroups have developed. The "Old Order Amish", a conservative faction that withdrew...

spelled backwards, and the agemo subgroup is denoted by an upside-down omega (℧). The omega subgroups are the series of subgroups of a finite p-group, G, indexed...

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...

definitions for a nilpotent 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...

French television series. This series is about a French special forces commando unit that must face Daesh and one of its subgroups that calls itself the...

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...

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...

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

field of group theory, a subgroup of a group is said to be descendant if there is a descending series starting from the subgroup and ending at the group...

In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. Let G {\displaystyle...

mod 3, so is a subgroup of the Chevalley group E8(3). The subgroup preserving the Lie bracket (over the integers) is a maximal subgroup of the Thompson...

groups, a Grosshans subgroup, named after Frank Grosshans, is an algebraic subgroup of an algebraic group that is an observable subgroup for which the ring...

Zoologists sometimes use additional terms such as "species group", "species subgroup", "species complex" and "superspecies" for convenience as extra, but unofficial...

BaAl2Si3O10·4H2O Erionite subgroup – (Na1−2,K1−2,Ca1−2)2Al4Si14O36·15H2O Faujasite subgroup – (Na1−2,Ca1−2,Mg1−2)3.5[Al7Si17O48]·32H2O Ferrierite subgroup – [Mg2(K,Na)2Ca0...

Alternatives are 4th level ATC chemical subgroup (C09AA ACE inhibitors, plain) (for lisinopril) and 4th level ATC chemical subgroup (C08CA Dihydropyridine derivatives)...

the upper central series. Generalizing the earlier comments about the socle, a finite p-group with order pn contains normal subgroups of order pi with...