Another Proof of Half Homomorphisms

Abstract

Scott proves in (Scott, 1957) that a half-homomorphism of a group is either a homomorphism or an anti-homomorphism. The proof given by Scott relies on properties of half-isomorphisms of a cancellation semi-group. In a different point of view, Mansfield proves that, in (Mansfield, 1992), a group determinant determines the underlying group. We give an alternate proof that a half-homomorphism of a group is either a homomorphism or an anti-homomorphism by using Manfields’s process to determine the underlying group of a group determinant. Keywords :  half-homomorphism, anti-homomorphism, group determinant