Automorphisms of graphs of groups with cyclic edge groups
Group Theory
2025-07-23 v1
Abstract
We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when edge groups are cyclic, and vertex groups are torsion-free with cyclic centralizers. We show that in this case the outer automorphism group is virtually built from the outer automorphisms of the vertex groups (fixing some elements), the outer automorphisms of some associated generalized Baumslag-Solitar groups, and generalized twists - partial conjugations by elements in the centralizers of some elliptic elements in the group.
Cite
@article{arxiv.2507.16489,
title = {Automorphisms of graphs of groups with cyclic edge groups},
author = {Dario Ascari and Montserrat Casals-Ruiz and Ilya Kazachkov},
journal= {arXiv preprint arXiv:2507.16489},
year = {2025}
}
Comments
20 pages, 3 figures