# Semantic search

Abelian automorphism group not implies cyclic, Cyclic and capable implies trivial, Cyclic automorphism group implies abelian, Cyclic automorphism group not implies cyclic, Cyclic implies abelian, Cyclic implies abelian automorphism group, Cyclic over central implies abelian, Cyclic subgroup of maximum order is direct factor in finite abelian group, Cyclicity is 2-local for finite groups, Cyclicity is subgroup-closed, Equivalence of definitions of cyclic group, Every Sylow subgroup is cyclic implies metacyclic, Finite abelian and abelian automorphism group implies cyclic, Finite and cyclic automorphism group implies cyclic, Finite group having the same order statistics as a cyclic group is cyclic, Finite group implies cyclic iff every subgroup is characteristic, Group in which every finite abelian subgroup is cyclic, Odd-order cyclic group equals derived subgroup of holomorph, Schur multiplier of cyclic group is trivial