On Product-Equality-Preserving Mappings in Groups Original Research Article

LetG, Hbe groups,Msubset of or equal toG. A mappingf:M→His called aProduct-equality-preserving(PEP)mappingiff it satisfies[formula] Timage. LetG1, G2be nonabelian groups with centersZ1, Z2and letM1, M2satisfy[formula]Letf:M1→M2be a PEP mapping that mapsM1ontoM2. Then there is an epimorphism phi:G1→G2andvset membership, variantZ2such that for everyxset membership, variantM1,[formula]