Category:Functional subgroups

From Wikipedia, the free encyclopedia

Given a group, there are some subgroups of interest that can be defined uniquely and functionally in terms of G, such as the center, commutator, etc. These should be invariant under isomorphisms, that is, any isomorphism on the groups, must induce a corresponding isomorphism on the subgroups. Hence, such subgroups are invariant under automorphisms, and are always characteristic subgroups.