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...

specific domains Characteristic polynomial, a polynomial associated with a square matrix in linear algebra Characteristic subgroup, a subgroup that is invariant...

In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...

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...

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...

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...

a group is said to be characteristically simple if it has no proper nontrivial characteristic subgroups. Characteristically simple groups are sometimes...

commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. The commutator subgroup is important...

(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...

The center is a normal subgroup, Z(G) ⊲ G, and also a characteristic subgroup, but is not necessarily fully characteristic. The quotient group, G /...