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...
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commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. The commutator subgroup is important...
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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...
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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...
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Theory. Krieger, 1975. Schmidt, Roland. Subgroup Lattices of Groups. de Gruyter, 1994. Keith Conrad, SUBGROUP SERIES II, Section 4 , http://www.math.uconn...
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Solvable group (redirect from Solvable subgroup)
Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory...
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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...
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Fitting length (redirect from Lower Fitting series)
investigations of nilpotent normal subgroups. A Fitting chain (or Fitting series or nilpotent series) for a group is a subnormal series with nilpotent quotients...
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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...
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In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...
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Core (group theory) (redirect from Core-free subgroup)
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...
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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...
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Descendant tree (group theory) (category Subgroup series)
{\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...
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2016. Retrieved January 30, 2017. "John Glenn Archives, Audiovisuals Subgroup, Series 3: Certificates". Ohio State University. Archived from the original...
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years, as Amish churches have divided many times over doctrinal disputes, subgroups have developed. The "Old Order Amish", a conservative faction that withdrew...
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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...
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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...
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Nilpotent group (redirect from Central series of a group)
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...
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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...
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Monster group (section Maximal subgroups)
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...
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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...
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Serpentine subgroup (part of the kaolinite-serpentine group in the category of phyllosilicates) are greenish, brownish, or spotted minerals commonly found...
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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...
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In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. Let G {\displaystyle...
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Thompson sporadic group (section Maximal subgroups)
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...
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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...
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Taxonomic rank (redirect from Species subgroup)
Zoologists sometimes use additional terms such as "species group", "species subgroup", "species complex" and "superspecies" for convenience as extra, but unofficial...
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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...
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Alternatives are 4th level ATC chemical subgroup (C09AA ACE inhibitors, plain) (for lisinopril) and 4th level ATC chemical subgroup (C08CA Dihydropyridine derivatives)...
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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...
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