The Existence of Strong Complete Mappings
Abstract
A strong complete mapping of a group G is a bijection θ:G→G for which both mappings x↦xθ(x) and x↦x−1θ(x) are bijections. We characterize finite abelian groups that admit strong complete mappings, thus solving a problem posed by Horton in 1990. We also prove the existence of strong complete mappings for countably infinite groups.
A corrigendum for this paper was added on 2 October 2018.