Generators and relations for subsemigroups via boundaries in Cayley graphs |
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Authors: | R Gray N Ruškuc |
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Institution: | a Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugalb School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK |
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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. |
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Keywords: | 20M05 |
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