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...

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...

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...

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...

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...

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...

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...

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

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

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...

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

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

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...

return the minimal word, but it can return optimal words based on the series of subgroups that is used. The code looks like this: function operate(element...

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...

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...

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 |...

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

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...

{\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...

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...

the Puig subgroup, introduced by Puig (1976), is a characteristic subgroup of a p-group analogous to the Thompson subgroup. If H is a subgroup of a group...

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...

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...

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...

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...

(or most) of the unitary dual could be parametrised by starting with a subgroup H of G, simpler but not compact, and building up induced representations...