# Semantic search

Center not is fully invariant in class two p-group, Characteristic direct factor not implies fully invariant, Characteristic equals fully invariant in odd-order abelian group, Characteristic not implies fully invariant, Characteristic not implies fully invariant in class three maximal class p-group, Characteristic not implies fully invariant in finite abelian group, Characteristic not implies fully invariant in finitely generated abelian group, Characteristic not implies fully invariant in odd-order class two p-group, Characteristic not implies potentially fully invariant, Equivalence of definitions of fully invariant direct factor, Every nontrivial characteristic subgroup is potentially characteristic-and-not-fully invariant, Every nontrivial normal subgroup is potentially characteristic-and-not-fully invariant, Finitary symmetric group is not fully invariant in symmetric group, Finite direct power-closed characteristic not implies fully invariant, Finite group implies cyclic iff every subgroup is characteristic, Full invariance does not satisfy image condition, Full invariance does not satisfy intermediate subgroup condition, Full invariance is finite direct power-closed, Full invariance is not direct power-closed, Full invariance is quotient-transitive