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Permutations of a semigroup that map to inverses

Higgins, Peter M (2014) 'Permutations of a semigroup that map to inverses.' Semigroup Forum, 89 (1). pp. 169-182. ISSN 0037-1912

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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.

Item Type: Article
Additional Information: 14 pages
Uncontrolled Keywords: Permutation matching; Hall's Marriage lemma; Full transformation semigroup; Finite regular semigroup
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 12 Nov 2014 14:10
Last Modified: 15 Jan 2022 00:29

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