Fixed points of endomorphisms of graph groups

Abstract

It is shown, for a given graph group G, that the fixed point subgroup Fix φ is finitely generated for every endomorphism φ of G if and only if G is a free product of free abelian groups. The same conditions hold for the subgroup of periodic points. Similar results are obtained for automorphisms if the dependence graph of G is a transitive forest. © de Gruyter 2013.