Generators and relations for subsemigroups via boundaries in Cayley graphs
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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.
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 . DOI: 10.1016/j.jpaa.2011.03.017
Journal of Pure and Applied Algebra
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