ON RECURSIVE PRESENTATIONS FOR GROUPS ACTING ON TREES WITH INVERSIONS

R. M. S. Mahmood (United Arab Emirates)

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.