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