- Title
- Computing the scale of an endomorphism of a totally disconnected locally compact group
- Creator
- Willis, George A.
- Relation
- Axioms Vol. 6, Issue 4, no. 27
- Publisher Link
- http://dx.doi.org/10.3390/axioms6040027
- Publisher
- MDPI AG
- Resource Type
- journal article
- Date
- 2017
- Description
- 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.
- Subject
- locally compact group; endomorphism; scale; tree; Neretin’s group; Thompson’s group; p-adic Lie group
- Identifier
- http://hdl.handle.net/1959.13/1385848
- Identifier
- uon:32304
- Identifier
- ISSN:2075-1680
- Rights
- © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
- Language
- eng
- Full Text
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