This group gathers theorems about groups, the algebraic structures that capture symmetry through a single operation with an identity and inverses. It covers results on the sizes and structure of subgroups, on how a group can be embedded in a permutation group, on composition and decomposition of groups into simpler pieces, on solvable and simple groups, and on the large classification of finite simple groups. A theorem belongs here when its cited article places it in group theory or states a result about groups and their subgroups. Results about rings, fields or matrices are grouped elsewhere under Algebra.
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Jordan-Holder Theorem (Wikipedia, Composition Series Article)
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Nevertheless, a group of results known under the general name Jordan-Hölder theorem asserts that whenever composition series exist, the isomorphism classes of simple pieces (although, perhaps, not their location in the composition series in question) and their multiplicities are uniquely determined.
Cauchy's Theorem (Group Theory) (Wikipedia)
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In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number of elements in G), then G contains an element of order p.
Lagrange's Theorem, Group Theory (Wikipedia)
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In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup
Wikipedia: Cayley's Theorem
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In the mathematical discipline of group theory, Cayley's theorem, named in honour of Arthur
Sylow Theorems (Wikipedia)
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In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems
Burnside's theorem (Wikipedia)
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G} is solvable. Hence each non-Abelian finite simple group has order divisible by at least three distinct
Feit-Thompson Theorem (Wikipedia)
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theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the
Classification of Finite Simple Groups (Wikipedia)
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(popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either
Nielsen-Schreier Theorem (Wikipedia)
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In group theory, a branch of mathematics, the Nielsen-Schreier
Wikipedia: Krull-Schmidt theorem
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subjected to certain finiteness conditions on chains of subgroups, can be uniquely written as a finite direct
Higman's embedding theorem (Wikipedia)
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In group theory, Higman's embedding theorem states that every
Commutator Subgroup (Wikipedia)
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more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup
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