Topologically simple, totally disconnected, locally compact infinite matrix groups

Title: Topologically simple, totally disconnected, locally compact infinite matrix groups
Creator: Groenhout, Peter; Reid, Colin D.; Willis, George A.
Relation: Journal of Lie Theory Vol. 30, Issue 4, p. 965-980
Relation: https://www.heldermann.de/JLT/JLT30/JLT304/jlt30047.htm
Publisher: Heldermann Verlag
Resource Type: journal article
Date: 2020
Description: We construct uncountably many non-locally isomorphic examples of topologically simple nondiscrete totally disconnected locally compact groups. The new examples differ from known examples of such groups in that they have trivial quasi-centre, but also have infinite abelian locally normal subgroups. The examples are constructed as almost upper-triangular matrices modulo scalar matrices over finite fields, where "almost upper-triangular" is defined with respect to one of an uncountable family of preorders generalising the natural orders on the set of integers and the set of natural numbers.
Subject: infinite matrix; finite field; locally compact group; topologically simple; quasi-centre
Identifier: http://hdl.handle.net/1959.13/1445880
Identifier: uon:42700
Identifier: ISSN:0949-5932
Language: eng
Reviewed