JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 1, Pages 1 - 16
(April 2005)
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ON RECURSIVE PRESENTATIONS FOR GROUPS ACTING ON TREES WITH INVERSIONS
R. M. S. Mahmood (United Arab Emirates)
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Abstract: In this paper we show that if G is a group acting on a tree X with inversions such that the vertex stabilizer for each vertex of X is recursively presented, the edge stabilizer for each edge of X is finitely generated, and the quotient graph X/G is finite, then G is recursively presented. The main technique used is Higman�s theorem which states that a finitely generated group is embeddable in a finitely presented group if and only if it is recursively presented. |
Keywords and phrases: groups acting on trees with inversions, Higman�s theorem, recursive presentations. |
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