Subgroups of Finitely Presented Centre-by-Metabelian Groups

Strebel, Ralph

doi:10.1112/jlms/s2-28.3.481

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2011

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“…In particular, we have the Reidemeister-Schreier theorem which says that subgroups of finitely presented groups with finite index are finitely presented; see [18,Proposition 4.2]. The general study of subgroups of finitely presented groups continues to receive a lot of attention; see for example [2,8,26]. An important problem in the development of a similar theory for arbitrary monoids has been the search for a suitable notion of index for subsemigroups.…”

Section: Introductionmentioning

confidence: 98%

Generators and relations for subsemigroups via boundaries in Cayley graphs

Gray

Ruškuc

2011

Journal of Pure and Applied Algebra

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a b s t r a c tGiven 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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Section: Introductionmentioning

confidence: 98%