The existence of strong complete mappings
AB Evans�- the electronic journal of combinatorics, 2012 - combinatorics.org
AB Evans
the electronic journal of combinatorics, 2012•combinatorics.orgA strong complete mapping of a group $ G $ is a bijection $\theta\colon G\to G $ for which
both mappings $ x\mapsto x\theta (x) $ and $ x\mapsto x^{-1}\theta (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.
both mappings $ x\mapsto x\theta (x) $ and $ x\mapsto x^{-1}\theta (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.
Abstract
A strong complete mapping of a group is a bijection for which both mappings and 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.
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