Next Article in Journal / Special Issue
Large Sets in Boolean and Non-Boolean Groups and Topology
Previous Article in Journal
From Normal Surfaces to Normal Curves to Geodesics on Surfaces
Previous Article in Special Issue
Categorically Closed Topological Groups
Article Menu

Export Article

Open AccessArticle
Axioms 2017, 6(4), 27; doi:10.3390/axioms6040027

Computing the Scale of an Endomorphism of a totally Disconnected Locally Compact Group

School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan NSW 2308, Australia
Received: 28 August 2017 / Revised: 9 October 2017 / Accepted: 9 October 2017 / Published: 20 October 2017
(This article belongs to the Collection Topological Groups)
View Full-Text   |   Download PDF [299 KB, uploaded 26 October 2017]   |  

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. 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. View Full-Text
Keywords: locally compact group; endomorphism; scale; tree; Neretin’s group; Thompson’s group; p-adic Lie group locally compact group; endomorphism; scale; tree; Neretin’s group; Thompson’s group; p-adic Lie group
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Willis, G.A. Computing the Scale of an Endomorphism of a totally Disconnected Locally Compact Group. Axioms 2017, 6, 27.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top