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# Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

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1435-5337
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Volume 28, Issue 5

# On the K-theory of certain extensions of free groups

Vassilis Metaftsis
/ Stratos Prassidis
Published Online: 2015-09-24 | DOI: https://doi.org/10.1515/forum-2014-0214

## Abstract

Since $Hol\left({F}_{n}\right)$ embeds into $Aut\left({F}_{n+1}\right)$, one can construct inductively the subgroups ${\mathcal{ℋ}}_{\left(n\right)}$ of $Aut\left({F}_{n+1}\right)$ by setting ${\mathcal{ℋ}}_{\left(1\right)}=Hol\left({F}_{2}\right)$ and ${\mathcal{ℋ}}_{\left(n\right)}={F}_{n+1}⋊{\mathcal{ℋ}}_{\left(n-1\right)}$. We show that the FJCw holds for ${\mathcal{ℋ}}_{\left(n\right)}$. Moreover, we calculate the lower K-theory for the groups ${\mathcal{ℋ}}_{\left(n\right)}$.

MSC 2010: 19D35; 20F65

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Revised: 2015-07-04

Published Online: 2015-09-24

Published in Print: 2016-09-01

Funding Source: European Social Fund

Award identifier / Grant number: THALIS

Research supported by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: THALIS.

Citation Information: Forum Mathematicum, Volume 28, Issue 5, Pages 813–822, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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