Geodesic
Topologically Simple, Totally Disconnected, Locally Compact Infinite Matrix Groups
Peter Groenhout1 ; George A. Willis1 ; Colin D. Reid1
1The University of Newcastle, Callaghan 2308, NSW, Australia
Journal of Lie Theory, Tome 30 (2020) no. 4, pp. 965-980

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22D05, 20H30, 20E18
Mots-clés : Infinite matrix, finite field, locally compact group, topologically simple, quasi-centre

Peter Groenhout  1   ; George A. Willis  1   ; Colin D. Reid  1

1 The University of Newcastle, Callaghan 2308, NSW, Australia 
Peter Groenhout; George A. Willis; Colin D. Reid. Topologically Simple, Totally Disconnected, Locally Compact Infinite Matrix Groups. Journal of Lie Theory, Tome 30 (2020) no. 4, pp. 965-980. http://geodesic.mathdoc.fr/item/JOLT_2020_30_4_a3/
@article{JOLT_2020_30_4_a3,
     author = {Peter Groenhout and George A. Willis and Colin D. Reid},
     title = {Topologically {Simple,} {Totally} {Disconnected,} {Locally} {Compact} {Infinite} {Matrix} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {965--980},
     year = {2020},
     volume = {30},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2020_30_4_a3/}
}
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