Permutations of a semigroup that map to inverses
Group Theory
2019-01-17 v1
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.
Cite
@article{arxiv.1901.05198,
title = {Permutations of a semigroup that map to inverses},
author = {Peter M. Higgins},
journal= {arXiv preprint arXiv:1901.05198},
year = {2019}
}
Comments
14 pages