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Contraction groups and passage to subgroups and quotients for endomorphisms of totally disconnected locally compact groups

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Abstract

The concepts of the scale and tidy subgroups for an automorphism of a totally disconnected locally compact group were defined in seminal work by George A. Willis in the 1990s, and recently generalized to the case of endomorphisms (G. A.Willis, Math. Ann. 361 (2015), 403–442). We show that central facts concerning the scale, tidy subgroups, quotients, and contraction groups of automorphisms extend to the case of endomorphisms. In particular, we obtain results concerning the domain of attraction around an invariant closed subgroup.

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Authors and Affiliations

  1. School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2006, Australia

    Timothy P. Bywaters

  2. Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098, Paderborn, Germany

    Helge Glöckner

  3. Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland

    Stephan Tornier

  4. School of Mathematical and Physical Sciences, The University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia

    Stephan Tornier

Authors
  1. Timothy P. Bywaters
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  2. Helge Glöckner
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  3. Stephan Tornier
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Correspondence to Stephan Tornier.

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Bywaters, T.P., Glöckner, H. & Tornier, S. Contraction groups and passage to subgroups and quotients for endomorphisms of totally disconnected locally compact groups. Isr. J. Math. 227, 691–752 (2018). https://doi.org/10.1007/s11856-018-1750-9

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  • DOI: https://doi.org/10.1007/s11856-018-1750-9

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