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Contraction Groups and Passage to Subgroups and Quotients for Endomorphisms of Totally Disconnected Locally Compact Groups

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Author Bywaters Timothy P., Glöckner Helge, Tornier Stephan,
Project Closure of projections of lattices in products of trees
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Original article (peer-reviewed)

Journal Israel Journal of Mathematics
Title of proceedings Israel Journal of Mathematics


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.