,"Difficulty level","Fact about"
"Finite groups are elementarily equivalent iff they are isomorphic",,"Elementarily equivalent groups; ?,Isomorphic groups; ?"
"Finitely generated abelian groups are elementarily equivalent iff they are isomorphic",,"Finitely generated abelian group; ?,Elementarily equivalent groups; ?,Isomorphic groups; ?"
"Isotopic groups are isomorphic",,"Isotopic magmas; ?,Isotopy of magmas; ?,Isomorphic magmas; ?,Isomorphism of magmas; ?,Isomorphic groups; ?,Isomorphism of groups; ?"
"There exist abelian groups whose isomorphism classes of direct powers have any given period",,"Group isomorphic to its cube; 2,Group isomorphic to its square; 2,Torsion-free abelian group; ?,Abelian group; ?,Torsion-free group; ?,Direct power of a group; ?,Isomorphic groups; ?,Group isomorphic to its cube; ?,Group isomorphic to its square; ?"