# Semantic search

2-subnormal implies conjugate-join-closed subnormal, 2-subnormal implies conjugate-permutable, 2-subnormal implies join-transitively subnormal, 2-subnormal not implies automorph-permutable, 2-subnormal not implies hypernormalized, 2-subnormal subgroup has a unique fastest ascending subnormal series, 2-subnormality is conjugate-join-closed, 2-subnormality is not finite-join-closed, 2-subnormality is not finite-upper join-closed, 2-subnormality is not transitive, 2-subnormality is strongly intersection-closed, 3-subnormal subgroup need not have a unique fastest ascending subnormal series, Abnormal normalizer and 2-subnormal not implies normal, Base of a wreath product implies right-transitively 2-subnormal, Base of a wreath product not implies elliptic, Centralizer of derived subgroup is hereditarily 2-subnormal, Cofactorial automorphism-invariant implies left-transitively 2-subnormal, Commutator of a 2-subnormal subgroup and a subset implies 3-subnormal, Commutator of a normal subgroup and a subset implies 2-subnormal, Elementary abelian-to-2-subnormal replacement theorem, Index four implies 2-subnormal or double coset index two, Left residual of 2-subnormal by normal is normal of characteristic, Normal closure of 2-subnormal subgroup of prime order in nilpotent group is abelian, Normal closure of 2-subnormal subgroup of prime order is abelian, Normal closure of 2-subnormal subgroup of prime power order in nilpotent group has nilpotency class at most equal to prime-base logarithm of order, Normal of characteristic of base of a wreath product with diagonal action implies 2-subnormal, Prime-base logarithm of order of 2-subnormal subgroup of group of prime power order gives upper bound on nilpotency class of its normal closure, Subgroup-cofactorial automorphism-invariant implies left-transitively 2-subnormal, Subnormality is not permuting upper join-closed