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...

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...

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...

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

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...

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...

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

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

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

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...

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

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...

{\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...

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...

algorithm works is by restricting the positions of the cubes into a subgroup series of cube positions that can be solved using a certain set of moves....

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

Cooper found a general approach that used the underlying modular congruence subgroup Γ 0 ( n ) {\displaystyle \Gamma _{0}(n)} , while G. Almkvist has experimentally...

only. Consistency is missing too on the group name endings (group, subgroup, series) between New Dana Classification and mindat.org. Category, class and...

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...

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...

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...

of Burundi On the eve of the conference the Congolese delegations held a series of meetings. Concern was expressed by Congolese students in Brussels that...

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

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...

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...

Khaladitka/Xaladytka Roma (Халадытка Рома; lit. 'Roma Soldiers'), are the largest subgroup of Romani people in Russia and Belarus, with smaller remnants of the group...