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Subsemigroups of virtually free groups: finite Malcev presentations and testing for freeness

  • ALAN J. CAIN (a1), EDMUND F. ROBERTSON (a1) and NIK RUšKUC (a1)
Abstract

This paper shows that, given a finite subset $X$ of a finitely generated virtually free group $F$, the freeness of the subsemigroup of $F$ generated by $X$ can be tested algorithmically. (A group is virtually free if it contains a free subgroup of finite index.) It is then shown that every finitely generated subsemigroup of $F$ has a finite Malcev presentation (a type of semigroup presentation which can be used to define any semigroup that embeds in a group), and that such a presentation can be effectively found from any finite generating set.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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