The Existence of Strong Complete Mappings

  • Anthony B. Evans

Abstract

A strong complete mapping of a group G is a bijection θ:GG for which both mappings xxθ(x) and xx1θ(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.

Published
2012-02-07
Article Number
P34