# Semantic search

Cauchy's theorem for abelian groups, Characteristic not implies fully invariant in finite abelian group, Commuting fraction more than five-eighths implies abelian, Cyclic subgroup of maximum order is direct factor in finite abelian group, Finite abelian and abelian automorphism group implies cyclic, Finite abelian groups with the same order statistics are isomorphic, Finite abelian implies same orbit sizes of conjugacy classes and irreducible representations under automorphism group, Fully invariant not implies verbal in finite abelian group, Group in which every finite abelian subgroup is cyclic, Nilpotent of cube-free order implies abelian, Series-equivalent not implies automorphic in finite abelian group, Subgroup lattice and quotient lattice of finite abelian group are isomorphic, There exists an abelian group of prime power order that is lattice-isomorphic to a non-abelian group not of prime power order