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Permutations of a semigroup that map to inverses

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Abstract

We investigate the question as to when the members of a finite regular semigroup may be permuted in such a way that each member is mapped to one of its inverses. In general this is not possible. However we reformulate the problem in terms of a related graph and, using an application of Hall’s Marriage Lemma, we show in particular that the finite full transformation semigroup does enjoy this property.

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Acknowledgements

The author would like to thank an anonymous referee of this paper for some enlightening observations that led to its improvement.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Essex, Essex, CO4 3SQ, UK

    Peter M. Higgins

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  1. Peter M. Higgins
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Correspondence to Peter M. Higgins.

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Communicated by Nik Ruskuc.

Dedicated to the memory of John M. Howie.

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Higgins, P.M. Permutations of a semigroup that map to inverses. Semigroup Forum 89, 169–182 (2014). https://doi.org/10.1007/s00233-013-9535-2

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  • DOI: https://doi.org/10.1007/s00233-013-9535-2

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