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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.
Original language  English 

Pages (fromto)  5766 
Number of pages  10 
Journal  Mathematical Proceedings of the Cambridge Philosophical Society 
Volume  141 
Issue number  1 
DOIs  
Publication status  Published  Jul 2006 
Keywords
 Contextfree languages
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Dive into the research topics of 'Subsemigroups of virtually free groups: finite Malcev presentations and testing for freeness'. Together they form a unique fingerprint.Projects
 1 Finished

EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications
Linton, S. A., Gent, I. P., Leonhardt, U., Mackenzie, A., Miguel, I. J., Quick, M. & Ruskuc, N.
1/09/05 → 31/08/10
Project: Standard