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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.
Original language  English 

Pages (fromto)  27612779 
Journal  Journal of Pure and Applied Algebra 
Volume  215 
Issue number  11 
Early online date  27 Mar 2011 
DOIs  
Publication status  Published  Nov 2011 
Keywords
 Semigroup
 Generators
 Presentations
 Cayley graph
 Subsemigroup
 ReidemeisterSchreier rewriting
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Dive into the research topics of 'Generators and relations for subsemigroups via boundaries in Cayley graphs'. Together they form a unique fingerprint.Projects
 3 Finished

Automata Languages Decidability: Automata, Languages, Decidability in Algebra
1/03/10 → 31/05/14
Project: Standard

Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids
Gray, R. D.
1/02/08 → 31/01/11
Project: Standard

EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications
Linton, S. A., Gent, I. P., Leonhardt, U., Mackenzie, A., Miguel, I. J., Quick, M. & Ruskuc, N.
1/09/05 → 31/08/10
Project: Standard