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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.

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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: http://eprints.soton.ac.uk/id/eprint/338952
DOI: doi:10.1515/jgt-2013-0050
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: 15 Mar 2024 03:29

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Contributors

Author: Goulnara Arzhantseva
Author: Jean-Francois Lafont
Author: Ashot Minasyan ORCID iD

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