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Directed graphs of inner translations of semigroups

Araújo, João; Bentz, Wolfram; Konieczny, Janusz


João Araújo

Janusz Konieczny


A mapping α: S → S is called a Cayley function if there exist an associative operation µ: S x S → S and an element a ϵ S such that α(x) = µ(a, x) for every x ϵ S. The aim of the paper is to give a characterization of Cayley functions in terms of their directed graphs. This characterization is used to determine which elements of the centralizer of a permutation on a finite set are Cayley functions. The paper ends with a number of problems.

Publication Date 2017-06
Journal Semigroup forum
Print ISSN 0037-1912
Electronic ISSN 1432-2137
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 94
Issue 3
Pages 650-673
Institution Citation Araújo, J., Bentz, W., & Konieczny, J. (2017). Directed graphs of inner translations of semigroups. Semigroup Forum, 94(3), 650-673.
Keywords Inner translations; Cayley functions; Functional digraphs
Publisher URL
Copyright Statement ©2017 University of Hull
Additional Information Authors' accepted manuscript of article published in: Semigroup forum, 2017, volume 94, issue 3. The final publication is available at Springer via


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