Annals of K-Theory
- Ann. K-Theory
- Volume 1, Number 4 (2016), 441-456.
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 -theoretic assembly map for the family of finite subgroups is split injective for every finitely generated linear group over a commutative ring with unit under the assumption that 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 exists.
Ann. K-Theory, Volume 1, Number 4 (2016), 441-456.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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