Fixed points of endomorphisms of graph groups

Abstract

It is shown, for a given graph group $G$, that the fixed point subgroup Fix$\phi$ is finitely generated for every endomorphism $\phi$ 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.

9 pages

Cited by in corpus (2)

• Finiteness results for subgroups of finite extensions
• Explicit bounds for fixed subgroups of endomorphisms of free products