# Semantic search

2-subnormal not implies automorph-permutable, Abelian normal not implies central, Central factor is not finite-intersection-closed, Central factor is not quotient-transitive, Characteristic not implies fully invariant, Characteristic not implies isomorph-free in finite group, Characteristic not implies isomorph-normal in finite group, Characteristically metacyclic not implies metacyclic derived series, Characteristicity does not satisfy image condition, Characteristicity does not satisfy intermediate subgroup condition, Characteristicity is not finite-relative-intersection-closed, Class two not implies abelian automorphism group, Complemented normal not implies direct factor, Conjugacy-closedness is not join-closed, Direct factor is not upper join-closed, Full invariance does not satisfy intermediate subgroup condition, Intermediate characteristicity is not transitive, Isomorph-freeness is not transitive, Lattice-complemented is not transitive, Left-transitively WNSCDIN not implies normal, Marginality does not satisfy intermediate subgroup condition, Nilpotent automorphism group not implies abelian automorphism group, Nilpotent not implies abelian, Normal not implies central factor, Normal not implies left-transitively fixed-depth subnormal, Normal not implies normal-extensible automorphism-invariant in finite, Normal not implies normal-potentially characteristic, Normal not implies normal-potentially relatively characteristic, Normal-extensible not implies normal, Normal-isomorph-free not implies isomorph-free in finite, Normality is not transitive, Omega-1 of odd-order class two p-group has prime exponent, Permutably complemented does not satisfy transfer condition, Permutably complemented is not finite-intersection-closed, Permutably complemented is not transitive, Potentially characteristic not implies normal-potentially characteristic, Pronormality is not centralizer-closed, Schur-triviality is not characteristic subgroup-closed, Schur-triviality is not subgroup-closed, Sylow not implies CDIN, Transitive normality is not quotient-transitive, Transitively normal not implies central factor