A weak Zassenhaus Lemma for discrete subgroups of Diff(I)

Akhmedov, Azer

doi:10.2140/agt.2014.14.539

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A weak Zassenhaus Lemma for discrete subgroups of $\operatorname{Diff}(I)$

Azer Akhmedov

Algebraic & Geometric Topology 14 (2014) 539–550

DOI: 10.2140/agt.2014.14.539

Abstract

We prove a weaker version of the Zassenhaus Lemma for subgroups of $Diff (I)$ . We also show that a group with commutator subgroup containing a non-Abelian free subsemigroup does not admit a $C_{0}$ –discrete faithful representation in $Diff (I)$ .

Keywords

diffeomorphism group of the interval, Zassenhaus Lemma, discrete subgroups of $\operatorname{Diff}(I)$

Mathematical Subject Classification 2010

Primary: 37C05

Secondary: 20F65

References

Publication

Received: 28 November 2012

Revised: 13 August 2013

Accepted: 15 August 2013

Published: 9 January 2014

Authors

Azer Akhmedov
Mathematics Department North Dakota State University Fargo, ND 58102 USA

Volume 14, issue 1 (2014)