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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Highly transitive actions of groups acting on trees
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by Pierre Fima, Soyoung Moon and Yves Stalder PDF
Proc. Amer. Math. Soc. 143 (2015), 5083-5095 Request permission

Abstract:

We show that a group acting on a non-trivial tree with finite edge stabilizers and icc vertex stabilizers admits a faithful and highly transitive action on an infinite countable set. This result is actually true for infinite vertex stabilizers and some more general, finite or infinite, edge stabilizers that we call highly core-free. We study the notion of highly core-free subgroups and give some examples. In the case of a free product amalgamated over a highly core-free subgroup and an HNN extension with a highly core-free base group we obtain a genericity result for faithful and highly transitive actions.
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  • Pierre Fima
  • Affiliation: Université Paris Diderot, Sorbonne Paris Cité, IMJ-PRG, UMR 7586, F-75013, Paris, France – and – Sorbonne Universités, UPMC Paris 06, UMR 7586, F-75013, Paris, France – and – CNRS, UMR 7586, IMJ-PRG, Case 7012, 75205 Paris, France
  • Email: pierre.fima@imj-prg.fr
  • Soyoung Moon
  • Affiliation: Institut Mathématiques de Bourgogne, Université de Bourgogne, CNRS UMR 5584, B.P. 47870, 21078 Dijon Cedex, France
  • Email: soyoung.moon@u-bourgogne.fr
  • Yves Stalder
  • Affiliation: Laboratoire de Mathématiques, Clermont Université, Université Blaise Pascal, BP 10448, F-63000 Clermont-Ferrand, France – and – CNRS UMR 6620, LM, F-63171 Aubière, France
  • Email: yves.stalder@math.univ-bpclermont.fr
  • Received by editor(s): November 27, 2013
  • Received by editor(s) in revised form: September 18, 2014
  • Published electronically: August 26, 2015
  • Additional Notes: The first author was partially supported by ANR Grants OSQPI and NEUMANN
    The second author was partially supported by FABER of Conseil Régional de Bourgogne
  • Communicated by: Kevin Whyte
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 5083-5095
  • MSC (2010): Primary 20B22; Secondary 20E06, 20E08, 43A07
  • DOI: https://doi.org/10.1090/proc/12659
  • MathSciNet review: 3411128