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On the K-theory of linear groups

On the K-theory of linear groups
On the K-theory of linear groups
We prove that for a finitely generated linear group over a field of positive characteristic the family of quotients by finite subgroups has finite asymptotic dimension. We use this to show that the K-theoretic assembly map for the family of finite subgroups is split injective for every finitely generated linear group G over a commutative ring with unit under the assumption that G admits a finite-dimensional model for the classifying space for the family of finite subgroups. Furthermore, we prove that this is the case if and only if an upper bound on the rank of the solvable subgroups of G exists.
2379-1691
441-456
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075

Kasprowski, Daniel (2016) On the K-theory of linear groups. Annals of K-Theory, 1 (4), 441-456. (doi:10.2140/akt.2016.1.441).

Record type: Article

Abstract

We prove that for a finitely generated linear group over a field of positive characteristic the family of quotients by finite subgroups has finite asymptotic dimension. We use this to show that the K-theoretic assembly map for the family of finite subgroups is split injective for every finitely generated linear group G over a commutative ring with unit under the assumption that G admits a finite-dimensional model for the classifying space for the family of finite subgroups. Furthermore, we prove that this is the case if and only if an upper bound on the rank of the solvable subgroups of G exists.

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Accepted/In Press date: 22 October 2015
Published date: 11 August 2016
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Identifiers

Local EPrints ID: 477749
URI: http://eprints.soton.ac.uk/id/eprint/477749
DOI: doi:10.2140/akt.2016.1.441
ISSN: 2379-1691
PURE UUID: 5d3f7be6-a83f-4741-95f1-4d749f540699
ORCID for Daniel Kasprowski: ORCID iD orcid.org/0000-0001-5926-2206

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Date deposited: 13 Jun 2023 17:32
Last modified: 17 Mar 2024 04:19

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Author: Daniel Kasprowski ORCID iD

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