Highly transitive actions of free products

Moon, Soyoung; Stalder, Yves

doi:10.2140/agt.2013.13.589

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Highly transitive actions of free products

Soyoung Moon and Yves Stalder

Algebraic & Geometric Topology 13 (2013) 589–607

DOI: 10.2140/agt.2013.13.589

Abstract

We characterize free products admitting a faithful and highly transitive action. In particular, we show that the group $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mo class="qopname"> PSL</mo></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo class="MathClass-open">(</mo><mrow><mi>ℤ</mi></mrow><mo class="MathClass-close">)</mo></mrow> <mo class="MathClass-rel">≃</mo> <mrow><mo class="MathClass-open">(</mo><mrow><mi>ℤ</mi><mo class="MathClass-bin">∕</mo><mn>2</mn><mi>ℤ</mi></mrow><mo class="MathClass-close">)</mo></mrow> <mo class="MathClass-bin">∗</mo> <mrow><mo class="MathClass-open">(</mo><mrow><mi>ℤ</mi><mo class="MathClass-bin">∕</mo><mn>3</mn><mi>ℤ</mi></mrow><mo class="MathClass-close">)</mo></mrow></math>$ admits a faithful and highly transitive action on a countable set.

Keywords

highly transitive actions, free products, Baire category Theorem

Mathematical Subject Classification 2010

Primary: 20B22, 20E06

References

Publication

Received: 16 May 2012

Revised: 16 October 2012

Accepted: 5 July 2012

Published: 23 March 2013

Authors

Soyoung Moon
Institut de Mathématiques de Bourgogne Université de Bourgogne UMR 5584 du CNRS, BP 47870 21078 Dijon France
http://moon.perso.math.cnrs.fr/
Yves Stalder
Laboratoire de Mathématiques Clermont Université, Université Blaise Pascal BP 10448 63000 Clermont-Ferrand France
http://math.univ-bpclermont.fr/~stalder/

Volume 13, issue 1 (2013)