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

Timothy P. Bywaters; Helge Glöckner; Stephan Tornier

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arXiv · 1612.06958

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

Timothy P. Bywaters·Helge Glöckner·Stephan Tornier

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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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Timothy P. Bywaters, Helge Glöckner, Stephan Tornier. 2017-09-14. Contraction Groups and Passage to Subgroups and Quotients for Endomorphisms of Totally Disconnected Locally Compact Groups. https://arxiv.org/abs/1612.06958

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