# Semantic search

Abelian central factor equals central subgroup, Abelian normal not implies central, Central implies abelian normal, Central implies finite-pi-potentially verbal in finite, Central implies image-potentially characteristic, Central implies normal, Central implies normal satisfying the subgroup-to-quotient powering-invariance implication, Central implies potentially characteristic, Central implies potentially fully invariant in finite, Central implies potentially verbal in finite, Central subgroup implies join-transitively central factor, Cyclic normal Sylow subgroup for least prime divisor is central, Join of Abelian and central implies Abelian, Join-transiter of Abelian is central, Minimal characteristic implies central in nilpotent, Minimal normal implies central in nilpotent group, Normal of order two implies central, Series-equivalent abelian-quotient central subgroups not implies automorphic, Series-equivalent characteristic central subgroups may be distinct, Sylow subgroups are in correspondence with Sylow subgroups of quotient by central subgroup