# Semantic search

Cyclicity is 2-local for finite groups, Equivalence of definitions of finitely generated group, Finitely generated abelian is subgroup-closed, Finitely generated and residually finite implies Hopfian, Finitely generated implies countable, Finitely generated implies every subgroup of finite index has finitely many automorphic subgroups, Finitely generated implies finitely many homomorphisms to any finite group, Finitely generated not implies Noetherian, Finitely generated not implies finitely presented, Finitely generated not implies residually finite, Free group on countable set is quotient-universal for finitely generated groups, Minimum size of generating set of extension group is bounded by sum of minimum size of generating set of normal subgroup and quotient group, Noetherian not implies finitely presented, Residually finite not implies finitely generated, Schreier's lemma