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Title: Generators and relations for subsemigroups via boundaries in Cayley graphs
Authors: Gray, R
Ruskuc, Nik
Keywords: Semigroup
Generators
Presentations
Cayley graph
Subsemigroup
Reidemeister-Schreier rewriting
QA Mathematics
Issue Date: Nov-2011
Citation: Gray , R & Ruskuc , N 2011 , ' Generators and relations for subsemigroups via boundaries in Cayley graphs ' Journal of Pure and Applied Algebra , vol 215 , no. 11 , pp. 2761-2779 .
Abstract: Given a finitely generated semigroup S and subsemigroup T of S we define the notion of the boundary of T in S which, intuitively, describes the position of T inside the left and right Cayley graphs of S. We prove that if S is finitely generated and T has a finite boundary in S then T is finitely generated. We also prove that if S is finitely presented and T has a finite boundary in S then T is finitely presented. Several corollaries and examples are given.
Version: Postprint
Status: Peer reviewed
URI: http://hdl.handle.net/10023/2131
DOI: http://dx.doi.org/10.1016/j.jpaa.2011.03.017
ISSN: 0022-4049
Type: Journal article
Rights: This is an author version of this article. The definitive version (c) 2011 Elsevier B.V. is available from www.sciencedirect.com
Appears in Collections:Centre for Interdisciplinary Research in Computational Algebra (CIRCA) Research
University of St Andrews Research
Pure Mathematics Research



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