English

Commensurating HNN-extensions: non-positive curvature and biautomaticity

Group Theory 2021-07-21 v4

Abstract

We show that the commensurator of any quasiconvex abelian subgroup in a biautomatic group is small, in the sense that it has finite image in the abstract commensurator of the subgroup. Using this criterion we exhibit groups that are CAT(0) but not biautomatic. These groups also resolve a number of other questions concerning CAT(0) groups.

Keywords

Cite

@article{arxiv.1907.03515,
  title  = {Commensurating HNN-extensions: non-positive curvature and biautomaticity},
  author = {Ian J. Leary and Ashot Minasyan},
  journal= {arXiv preprint arXiv:1907.03515},
  year   = {2021}
}

Comments

v4: 41 pages, re-formatted in G&T style. Some misprints have been corrected and references to recent results by other authors have been added