Annals of K-Theory

On the $K$-theory of linear groups

Daniel Kasprowski

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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.

Article information

Source
Ann. K-Theory, Volume 1, Number 4 (2016), 441-456.

Dates
Received: 8 May 2015
Revised: 20 September 2015
Accepted: 22 October 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.akt/1510841599

Digital Object Identifier
doi:10.2140/akt.2016.1.441

Mathematical Reviews number (MathSciNet)
MR3536434

Zentralblatt MATH identifier
06617209

Subjects
Primary: 18F25: Algebraic $K$-theory and L-theory [See also 11Exx, 11R70, 11S70, 12- XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 19A31: $K_0$ of group rings and orders 19B28: $K_1$of group rings and orders [See also 57Q10] 19G24: $L$-theory of group rings [See also 11E81]

Keywords
$K$- and $L$-theory of group rings injectivity of the assembly map linear groups

Citation

Kasprowski, Daniel. On the $K$-theory of linear groups. Ann. K-Theory 1 (2016), no. 4, 441--456. doi:10.2140/akt.2016.1.441. https://projecteuclid.org/euclid.akt/1510841599


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