# Semantic search

Abelian implies nilpotent, Ambivalent and nilpotent implies 2-group, C-closed implies completely divisibility-closed in nilpotent group, CA not implies nilpotent, Commutator-verbal implies divisibility-closed in nilpotent group, Commuting fraction more than half implies nilpotent, Comparable with all normal subgroups implies normal in nilpotent group, Derived length gives no upper bound on nilpotency class, Derived length is logarithmically bounded by nilpotency class, Derived subgroup not is intermediately powering-invariant in nilpotent group, Divisibility-closedness is strongly join-closed in nilpotent group, Epicentral series members are completely divisibility-closed in nilpotent group, Equivalence of definitions of nilpotent group, Equivalence of definitions of periodic nilpotent group, Finite non-nilpotent and every proper subgroup is nilpotent implies not simple, Group with nilpotent derived subgroup, Intermediately automorph-conjugate implies intermediately characteristic in nilpotent, Intermediately normal-to-characteristic implies intermediately characteristic in nilpotent, Isoclinic groups have same nilpotency class, Isologic groups with respect to fixed nilpotency class lower than theirs have equal nilpotency class, Local powering-invariant subgroup containing the center is intermediately local powering-invariant in nilpotent group, Locally nilpotent not implies nilpotent, Lower central series is fastest descending central series, Lower central series is strongly central, Maximal among abelian characteristic not implies self-centralizing in nilpotent, Maximal among abelian normal implies self-centralizing in nilpotent, Minimal normal implies central in nilpotent group, Nilpotency is 2-local for finite groups, Nilpotency of fixed class is quotient-closed, Nilpotency of fixed class is subgroup-closed, Nilpotent Hall implies isomorph-conjugate, Nilpotent and every abelian characteristic subgroup is central implies class at most two, Nilpotent automorphism group implies nilpotent of class at most one more, Nilpotent implies center is normality-large, Nilpotent implies derived in Frattini, Nilpotent implies every maximal subgroup is normal, Nilpotent implies every nontrivial normal subgroup contains a cyclic normal subgroup, Nilpotent implies every normal subgroup is potentially characteristic, Nilpotent implies every subgroup is subnormal, Nilpotent implies no proper contranormal subgroup, Nilpotent implies normalizer condition, Nilpotent join of intermediately isomorph-conjugate subgroups is intermediately isomorph-conjugate, Nilpotent join of pronormal subgroups is pronormal, Nilpotent not implies ACIC, Nilpotent not implies UL-equivalent, Nilpotent not implies abelian, Nilpotent not implies generated by abelian normal subgroups, Nilpotent not implies nilpotent automorphism group, Normalizer condition not implies nilpotent, P-group not implies nilpotent