in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is mapped to itself by every automorphism of the parent...
10 KB (1,191 words) - 16:31, 29 June 2022
specific domains Characteristic polynomial, a polynomial associated with a square matrix in linear algebra Characteristic subgroup, a subgroup that is invariant...
2 KB (258 words) - 09:13, 11 October 2021
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
examples section). If A is abelian, then the torsion subgroup T is a fully characteristic subgroup of A and the factor group A/T is torsion-free. There...
7 KB (911 words) - 21:28, 31 July 2024
want to prove that C is contained in H. If not, pick a minimal characteristic subgroup M/Z(H) of C/Z(H), where Z(H) is the center of H, which is the same...
9 KB (1,318 words) - 01:46, 6 September 2022
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
a group is said to be characteristically simple if it has no proper nontrivial characteristic subgroups. Characteristically simple groups are sometimes...
2 KB (209 words) - 12:24, 5 February 2024
commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. The commutator subgroup is important...
11 KB (1,833 words) - 17:10, 24 April 2023
Orthogonal group (section Lie subgroups)
(where I is the identity matrix) is a normal subgroup and even a characteristic subgroup of O(n), and, if n is even, also of SO(n). If n is odd, O(n) is...
56 KB (7,844 words) - 08:45, 30 June 2024
Center (group theory) (category Functional subgroups)
The center is a normal subgroup, Z(G) ⊲ G, and also a characteristic subgroup, but is not necessarily fully characteristic. The quotient group, G /...
12 KB (1,184 words) - 20:06, 14 May 2024