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2021 Commensurating HNN extensions: nonpositive curvature and biautomaticity
Ian J Leary, Ashot Minasyan
Geom. Topol. 25(4): 1819-1860 (2021). DOI: 10.2140/gt.2021.25.1819

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.

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Ian J Leary. Ashot Minasyan. "Commensurating HNN extensions: nonpositive curvature and biautomaticity." Geom. Topol. 25 (4) 1819 - 1860, 2021. https://doi.org/10.2140/gt.2021.25.1819

Information

Received: 23 July 2019; Revised: 18 June 2020; Accepted: 20 June 2020; Published: 2021
First available in Project Euclid: 12 October 2021

Digital Object Identifier: 10.2140/gt.2021.25.1819

Subjects:
Primary: 20F10 , 20F67
Secondary: 20E06

Keywords: biautomatic group , CAT(0) group , commensurating HNN extension

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 4 • 2021
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