# Semantic search

Automorphism group of finite nilpotent group is direct product of automorphism groups of Sylow subgroups, Classification of finite solvable CN-groups, Commutator of finite nilpotent group with coprime automorphism group equals second commutator, Commuting fraction more than half implies nilpotent, Comparable with all normal subgroups implies characteristic in finite nilpotent group, Conjecture that most finite groups are nilpotent, Core-free and permutable implies subdirect product of finite nilpotent groups, Degree of irreducible representation divides index of abelian subgroup in finite nilpotent group, Equivalence of definitions of finite nilpotent group, Finite nilpotent and every automorphism is inner implies trivial or cyclic of order two, Finite nilpotent implies every normal subgroup is part of a chief series, Finite non-nilpotent and every proper subgroup is nilpotent implies not simple, Nilpotency is 2-local for finite groups, Nilpotent of cube-free order implies abelian, Order statistics of a finite group determine whether it is nilpotent, Outer automorphism group of finite nilpotent group is direct product of outer automorphism groups of Sylow subgroups, Pyber's theorem on logarithmic quotient of number of nilpotent groups to number of groups approaching unity, Schmidt-Iwasawa theorem, Square of degree of irreducible representation divides order of inner automorphism group in finite nilpotent group, There exists an abelian group of prime power order that is lattice-isomorphic to a non-abelian group not of prime power order, Zorn's theorem on Engel groups