Ends of semigroups

Craik, S., Gray, R., Kilibarda, V., Mitchell, J. and Ruškuc, N. (2016) Ends of semigroups. Semigroup Forum, 93 (2). pp. 330-346. ISSN 0037-1912

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Abstract

We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by subsemigroups and extensions of finite Rees index. We prove an analogue of Hopf’s Theorem, stating that an infinite group has 1, 2 or infinitely many ends, for left cancellative semigroups and that the cardinality of the set of ends is invariant in subsemigroups and extension of finite Green index in left cancellative semigroups.

Item Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Uncontrolled Keywords: digraph,ends,cayley graph
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 29 Apr 2016 23:05
Last Modified: 22 Jul 2020 00:49
URI: https://ueaeprints.uea.ac.uk/id/eprint/58521
DOI: 10.1007/s00233-016-9814-9

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