no. 17-18
Group theory
Locally normal subgroups of simple locally compact groups
[Sous-groupes localement normaux des groupes localement compacts simples]

Présenté par : the Editorial Board

Caprace, Pierre-Emmanuel1 ; Reid, Colin D.2 ; Willis, George A.2
1 Université catholique de Louvain, IRMP, chemin du Cyclotron, 2, bte L7.01.02, B-1348 Louvain-la-Neuve, Belgium
2 Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, Australia
Comptes Rendus. Mathématique, Tome 351 (2013) no. 17-18, pp. 657-661.

On annonce divers résultats concernant la structure de groupes localement compacts, simples et compactement engendrés. Un invariant local de ces groupes, appelé treillis structurel, est introduit ; il consiste en des classes de commensurabilité de sous-groupes compacts à normalisateur ouvert. Les propriétés de ce treillis refètent la structure globale du groupe ambiant.

We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with open normaliser, and show that its properties reflect the global structure of the ambient group.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.09.010
Caprace, Pierre-Emmanuel 1 ; Reid, Colin D. 2 ; Willis, George A. 2

1 Université catholique de Louvain, IRMP, chemin du Cyclotron, 2, bte L7.01.02, B-1348 Louvain-la-Neuve, Belgium
2 Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, Australia 
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Caprace, Pierre-Emmanuel; Reid, Colin D.; Willis, George A. Locally normal subgroups of simple locally compact groups. Comptes Rendus. Mathématique, Tome 351 (2013) no. 17-18, pp. 657-661. doi : 10.1016/j.crma.2013.09.010. http://www.numdam.org/articles/10.1016/j.crma.2013.09.010/

[1] Barnea, Y.; Ershov, M.; Weigel, T. Abstract commensurators of profinite groups, Trans. Amer. Math. Soc., Volume 363 (2011) no. 10, pp. 5381-5417

[2] Caprace, P.-E.; Reid, C.D.; Willis, G.A. Locally normal subgroups of totally disconnected groups. Part I: General theory (available at) | arXiv

[3] Juschenko, K.; Monod, N. Cantor systems, piecewise translations and simple amenable groups, Ann. Math., Volume 178 (2013) no. 2, pp. 775-787

[4] Wilson, J.S. On just infinite abstract and profinite groups (du Sautoy, M.; Segal, D.; Shalev, A., eds.), New Horizons in Pro-p Groups, Birkhäuser, 2000 (chapter 5)

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