# Semantic search

Central factor not implies direct factor, Characteristic direct factor not implies fully invariant, Characteristic not implies direct factor, Complemented central factor not implies direct factor, Complemented normal not implies direct factor, Conjugacy-closed subgroup of ambivalent group is ambivalent, Cyclic subgroup of maximum order is direct factor in finite abelian group, Direct factor implies central factor, Direct factor implies join-transitively central factor, Direct factor implies normal, Direct factor implies right-quotient-transitively central factor, Direct factor implies transitively normal, Direct factor is not finite-join-closed, Direct factor is not upper join-closed, Direct factor is quotient-transitive, Direct factor is transitive, Direct factor not implies amalgam-characteristic, Direct factor not implies characteristic, Direct factor satisfies intermediate subgroup condition, Direct factor satisfies lower central series condition, Equivalence of definitions of fully invariant direct factor, Induced class function from conjugacy-closed normal subgroup is index of subgroup times class function inside the subgroup and zero outside the subgroup, Maximal among abelian normal subgroups of Sylow subgroup implies direct factor of centralizer, Normal not implies direct factor, Pure subgroup of torsion-free abelian group not implies direct factor