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.
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Pierre-Emmanuel Caprace 1 ; Colin D. Reid 2 ; George A. Willis 2
@article{CRMATH_2013__351_17-18_657_0, author = {Pierre-Emmanuel Caprace and Colin D. Reid and George A. Willis}, title = {Locally normal subgroups of simple locally compact groups}, journal = {Comptes Rendus. Math\'ematique}, pages = {657--661}, publisher = {Elsevier}, volume = {351}, number = {17-18}, year = {2013}, doi = {10.1016/j.crma.2013.09.010}, language = {en}, }
TY - JOUR AU - Pierre-Emmanuel Caprace AU - Colin D. Reid AU - George A. Willis TI - Locally normal subgroups of simple locally compact groups JO - Comptes Rendus. Mathématique PY - 2013 SP - 657 EP - 661 VL - 351 IS - 17-18 PB - Elsevier DO - 10.1016/j.crma.2013.09.010 LA - en ID - CRMATH_2013__351_17-18_657_0 ER -
Pierre-Emmanuel Caprace; Colin D. Reid; George A. Willis. Locally normal subgroups of simple locally compact groups. Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 657-661. doi : 10.1016/j.crma.2013.09.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.09.010/
[1] Abstract commensurators of profinite groups, Trans. Amer. Math. Soc., Volume 363 (2011) no. 10, pp. 5381-5417
[2] Locally normal subgroups of totally disconnected groups. Part I: General theory (available at) | arXiv
[3] Cantor systems, piecewise translations and simple amenable groups, Ann. Math., Volume 178 (2013) no. 2, pp. 775-787
[4] On just infinite abstract and profinite groups (M. du Sautoy; D. Segal; A. Shalev, eds.), New Horizons in Pro-p Groups, Birkhäuser, 2000 (chapter 5)
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