
Journal of Lie Theory 30 (2020), No. 4, 965980 Copyright Heldermann Verlag 2020 Topologically Simple, Totally Disconnected, Locally Compact Infinite Matrix Groups Peter Groenhout The University of Newcastle, Callaghan 2308, NSW, Australia peter.groenhout@uon.edu.au George A. Willis The University of Newcastle, Callaghan 2308, NSW, Australia george.willis@newcastle.edu.au Colin D. Reid The University of Newcastle, Callaghan 2308, NSW, Australia colin@reidit.net We construct uncountably many nonlocally 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 quasicentre, but also have infinite abelian locally normal subgroups. The examples are constructed as almost uppertriangular matrices modulo scalar matrices over finite fields, where "almost uppertriangular" 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. Keywords: Infinite matrix, finite field, locally compact group, topologically simple, quasicentre. MSC: 22D05; 20H30, 20E18. [ Fulltextpdf (149 KB)] for subscribers only. 