# 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, Full invariance is strongly join-closed, Full invariance is transitive, Fully invariant implies characteristic, Fully invariant implies finite direct power-closed characteristic, Fully invariant implies verbal in reduced free group, Fully invariant not implies abelian-potentially verbal in abelian group, Fully invariant not implies verbal in finite abelian group, Fully invariant of strictly characteristic implies strictly characteristic, Fully invariant subgroup of abelian group not implies divisibility-closed, Fully invariant subgroup of additive group of Lie ring is derivation-invariant and fully invariant, Fully invariant upper-hook EEP implies fully invariant, Homocyclic normal implies potentially fully invariant in finite, Image-closed characteristic not implies fully invariant, No subgroup property between normal Sylow and subnormal or between Sylow retract and retract is conditionally lattice-determined, Odd-order abelian group not is fully invariant in holomorph, Odd-order cyclic group is fully invariant in holomorph, Odd-order elementary abelian group is fully invariant in holomorph, Self-centralizing and minimal normal implies fully invariant in co-Hopfian group, Socle not is fully invariant in class two p-group, Special linear group is fully characteristic in general linear group, Strictly characteristic not implies fully invariant, Verbal implies fully invariant