theory, a Hall subgroup of a finite group G is a subgroup whose order is coprime to its index. They were introduced by the group theorist Philip Hall (1928)...
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as "H is a subgroup of G". The trivial subgroup of any group is the subgroup {e} consisting of just the identity element. A proper subgroup of a group...
20 KB (1,608 words) - 01:36, 28 January 2024
In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...
19 KB (3,157 words) - 18:43, 9 May 2024
abelian subgroups of |G|. This pattern of partitioning the prime divisors of |G| according to conjugacy classes of certain Hall subgroups (a Hall subgroup is...
21 KB (2,854 words) - 00:06, 12 March 2024
Sylow theorems (redirect from Sylow subgroup)
{\displaystyle p} , a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G {\displaystyle G} is a maximal p {\displaystyle p} -subgroup of G {\displaystyle...
33 KB (4,390 words) - 19:14, 2 April 2024
Three subgroups lemma Hall algebra, and Hall polynomials Hall subgroup Hall–Higman theorem Hall–Littlewood polynomial Hall's universal group Hall's marriage...
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{\displaystyle G/N} . An alternative statement of the theorem is that any normal Hall subgroup N {\displaystyle N} of a finite group G {\displaystyle G} has a complement...
10 KB (1,414 words) - 13:07, 23 May 2024
graph. The Hall–Janko graph was originally constructed by D. Wales to establish the existence of the Hall-Janko group as an index 2 subgroup of its automorphism...
3 KB (343 words) - 19:28, 28 July 2018
group theory, the Frattini subgroup Φ ( G ) {\displaystyle \Phi (G)} of a group G is the intersection of all maximal subgroups of G. For the case that G...
4 KB (476 words) - 00:53, 22 February 2024
Lie group (redirect from Lie subgroup)
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...
64 KB (9,427 words) - 05:48, 28 May 2024