The University of Southampton
University of Southampton Institutional Repository

Isomorphism versus commensurability for a class of finitely presented groups

Isomorphism versus commensurability for a class of finitely presented groups
Isomorphism versus commensurability for a class of finitely presented groups
We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability problem is solvable but the isomorphism problem is unsolvable. These are first examples of such a contrastive complexity behaviour with respect to the isomorphism problem.
Commensurable groups, virtual isomorphism problem, groups without finite quotients
1433-5883
361-378
Arzhantseva, Goulnara
cb099fac-8639-46ef-bac8-a93f68309758
Lafont, Jean-Francois
268f5958-24b9-4224-8f04-12a2c7ea20c8
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Arzhantseva, Goulnara
cb099fac-8639-46ef-bac8-a93f68309758
Lafont, Jean-Francois
268f5958-24b9-4224-8f04-12a2c7ea20c8
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d

Arzhantseva, Goulnara, Lafont, Jean-Francois and Minasyan, Ashot (2014) Isomorphism versus commensurability for a class of finitely presented groups. Journal of Group Theory, 17 (2), 361-378. (doi:10.1515/jgt-2013-0050).

Record type: Article

Abstract

We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability problem is solvable but the isomorphism problem is unsolvable. These are first examples of such a contrastive complexity behaviour with respect to the isomorphism problem.

Text
isom-6.pdf - Author's Original
Download (132kB)
Text
isom-7 - Accepted Manuscript
Download (146kB)

More information

Submitted date: September 2011
Accepted/In Press date: 8 May 2013
Published date: March 2014
Keywords: Commensurable groups, virtual isomorphism problem, groups without finite quotients
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 338952
URI: https://eprints.soton.ac.uk/id/eprint/338952
ISSN: 1433-5883
PURE UUID: d1edb925-4c34-4522-ba93-34545888550a
ORCID for Ashot Minasyan: ORCID iD orcid.org/0000-0002-4986-2352

Catalogue record

Date deposited: 21 May 2012 10:43
Last modified: 31 Jul 2019 00:39

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×