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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    CAIN, ALAN J. and MALTCEV, VICTOR 2016. GROWTHS OF ENDOMORPHISMS OF FINITELY GENERATED SEMIGROUPS. Journal of the Australian Mathematical Society, p. 1.


    Cain, Alan J. 2013. Automatic structures for subsemigroups of Baumslag–Solitar semigroups. Semigroup Forum, Vol. 87, Issue. 3, p. 537.


    Cain, Alan J. 2009. Malcev presentations for subsemigroups of direct products of coherent groups. Journal of Pure and Applied Algebra, Vol. 213, Issue. 6, p. 977.


    CAIN, ALAN J. ROBERTSON, EDMUND F. and RUŠKUC, NIK 2008. CANCELLATIVE AND MALCEV PRESENTATIONS FOR FINITE REES INDEX SUBSEMIGROUPS AND EXTENSIONS. Journal of the Australian Mathematical Society, Vol. 84, Issue. 01,


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 141, Issue 1
  • July 2006, pp. 57-66

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

  • ALAN J. CAIN (a1), EDMUND F. ROBERTSON (a1) and NIK RUšKUC (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004106009236
  • Published online: 03 July 2006
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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