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Keywords = Neretin’s group

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17 pages, 299 KB  
Article
Computing the Scale of an Endomorphism of a totally Disconnected Locally Compact Group
by George A. Willis
Axioms 2017, 6(4), 27; https://doi.org/10.3390/axioms6040027 - 20 Oct 2017
Cited by 2 | Viewed by 5935
Abstract
The scale of an endomorphism of a totally disconnected, locally compact group G is defined and an example is presented which shows that the scale function is not always continuous with respect to the Braconnier topology on the automorphism group of G. [...] Read more.
The scale of an endomorphism of a totally disconnected, locally compact group G is defined and an example is presented which shows that the scale function is not always continuous with respect to the Braconnier topology on the automorphism group of G. Methods for computing the scale, which is a positive integer, are surveyed and illustrated by applying them in diverse cases, including when G is compact; an automorphism group of a tree; Neretin’s group of almost automorphisms of a tree; and a p-adic Lie group. The information required to compute the scale is reviewed from the perspective of the, as yet incomplete, general theory of totally disconnected, locally compact groups. Full article
(This article belongs to the Collection Topological Groups)
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