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arXiv · 1210.4094

Fixed points of endomorphisms of graph groups

Emanuele Rodaro·Pedro V. Silva·Mihalis Sykiotis
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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.

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Emanuele Rodaro, Pedro V. Silva, Mihalis Sykiotis. 2012-10-15. Fixed points of endomorphisms of graph groups. https://doi.org/10.1515/jgt-2012-0047

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