Properties of groups inherited by normal subgroups (Q1105039)

Consider a group A with minimal condition on G-invariant subgroups, where G is a hypercentral automorphism group of A. Assume A to be the union of an ascending series of G-invariant subgroups with finite factors. Let H be a normal subgroup in G such that G/H is periodic. Then A has minimal condition on H-invariant subgroups. Consider a group B with finite automorphism group C such that every normal C-invariant subgroup in B is complemented. Then any normal subgroup in B is complemented.