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
In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group...
20 KB (1,637 words) - 10:11, 11 August 2024
Symmetric group (redirect from Transitive subgroup)
form a subgroup of index 2 in S, called the alternating subgroup A. Since A is even a characteristic subgroup of S, it is also a normal subgroup of the...
46 KB (6,130 words) - 06:34, 24 May 2024
important because it is the smallest normal subgroup such that the quotient group of the original group by this subgroup is abelian. In other words, G / N...
11 KB (1,833 words) - 17:10, 24 April 2023
monomorphism f from H to G is normal if and only if its image is a normal subgroup of G. In particular, if H is a subgroup of G, then the inclusion map...
2 KB (280 words) - 15:46, 13 February 2022
Core (group theory) (redirect from Core-free subgroup)
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 G, the normal core...
8 KB (1,149 words) - 23:28, 30 December 2023
group theory, the Fitting subgroup F of a finite group G, named after Hans Fitting, is the unique largest normal nilpotent subgroup of G. Intuitively, it...
9 KB (1,318 words) - 01:46, 6 September 2022
{\displaystyle gHg^{-1}} of a subgroup H in G is equal to the index of the normalizer of H in G. If H is a subgroup of G, the index of the normal core of H satisfies...
16 KB (2,596 words) - 12:53, 11 May 2023
field of group theory, a subgroup H {\displaystyle H} of a group G {\displaystyle G} is called c-normal if there is a normal subgroup T {\displaystyle T} of...
895 bytes (126 words) - 22:11, 1 October 2023
series (also normal series, normal tower, subinvariant series, or just series) of a group G is a sequence of subgroups, each a normal subgroup of the next...
9 KB (1,346 words) - 11:31, 12 September 2021