Subsemigroups of virtually free groups : finite Malcev presentations and testing for freeness
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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.
Cain , A J , Robertson , E F & Ruskuc , N 2006 , ' Subsemigroups of virtually free groups : finite Malcev presentations and testing for freeness ' Mathematical Proceedings of the Cambridge Philosophical Society , vol 141 , no. 1 , pp. 57-66 . DOI: 10.1017/S0305004106009236
Mathematical Proceedings of the Cambridge Philosophical Society
(c)2006 Cambridge Philosophical Society
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