Geodesic
The existence of strong complete mappings
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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A 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. A corrigendum for this paper was added on 2 October 2018.
DOI : 10.37236/2038
Classification : 20K01, 20K30
Mots-clés : finite abelian groups, strong complete mappings, countably infinite groups 
@article{10_37236_2038,
     author = {Anthony B. Evans},
     title = {The existence of strong complete mappings},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/2038},
     zbl = {1243.05050},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2038/}
}
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Anthony B. Evans. The existence of strong complete mappings. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/2038

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