# Semantic search

Equivalence of definitions of fully invariant direct factor, Equivalence of definitions of intermediately characteristic subgroup of finite abelian group, Finite cyclic and homomorph-containing implies order-unique, Finite group implies cyclic iff every subgroup is characteristic, Homomorph-containing not implies no nontrivial homomorphism to quotient group, Homomorph-containment is finite direct power-closed, Homomorph-containment is not transitive, Homomorph-containment is quotient-transitive, Homomorph-containment is strongly join-closed, Homomorph-containment satisfies intermediate subgroup condition, Subhomomorph-containing implies right-transitively homomorph-containing, Subisomorph-containing not implies homomorph-containing