Approximate homomorphisms II: Group homomorphisms

Abstract

We investigate mappings between finite product groups which are approximately homomorphisms, with respect to some metric on the range. Our main positive result says that if the metric corresponds to a nonpathological submeasure, then the mapping can be approximated by a homomorphism within a constant error. We also use Ramsey's theorem to prove that this fails in the case when the nonpathologicity assumption is dropped. This note extends results of [2], where analogous results were proved for Boolean algebras.