Directed graphs of inner translations of semigroups

Araújo, João; Bentz, Wolfram; Konieczny, Janusz

Abstract

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.

Citation

Araújo, J., Bentz, W., & Konieczny, J. (2017). Directed graphs of inner translations of semigroups. Semigroup Forum, 94(3), 650-673. https://doi.org/10.1007/s00233-016-9821-x

• Acceptance Date: Aug 11, 2016
• Online Publication Date: Aug 29, 2016
• Publication Date: 2017-06
• Deposit Date: Aug 24, 2016
• Publicly Available Date: Aug 29, 2016
• Journal: Semigroup forum
• Print ISSN: 0037-1912
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 94
• Issue: 3
• Pages: 650-673
• DOI: https://doi.org/10.1007/s00233-016-9821-x
• Keywords: Inner translations; Cayley functions; Functional digraphs
• Public URL: https://hull-repository.worktribe.com/output/442544
• Publisher URL: http://link.springer.com/article/10.1007%2Fs00233-016-9821-x
• Additional Information: Authors' accepted manuscript of article published in: Semigroup forum, 2017, volume 94, issue 3. The final publication is available at Springer via http://dx.doi.org/10.1007/s00233-016-9821-x
• Contract Date: Aug 24, 2016