Commensurators of abelian subgroups of biautomatic groups
Group Theory
2024-05-14 v3
Abstract
We show that the commensurator of any finitely generated abelian subgroup in a biautomatic group centralises a finite-index subgroup of . We deduce that the CAT(0) groups introduced by Leary-Minasyan are either biautomatic or cannot arise as subgroups of biautomatic groups, answering a question posed by Leary-Minasyan and generalising an analogous result for Baumslag-Solitar groups. These are the first examples of CAT(0) groups that are not subgroups of biautomatic groups.
Keywords
Cite
@article{arxiv.2104.13688,
title = {Commensurators of abelian subgroups of biautomatic groups},
author = {Motiejus Valiunas},
journal= {arXiv preprint arXiv:2104.13688},
year = {2024}
}
Comments
15 pages, 1 figure; v2: references updated; v3: a minor revision reflecting the referee's comments. Comments are welcome!