Approximating Simple Locally Compact Groups by Their Dense Locally Compact Subgroups

被引:4
|
作者
Caprace, Pierre-Emmanuel [1 ]
Reid, Colin [2 ]
Wesolek, Phillip [3 ]
机构
[1] Catholic Univ Louvain, IRMP, Chemin Cyclotron 2,Bte L7-01-02, B-1348 Louvain La Neuve, Belgium
[2] Univ Newcastle, Sch Math & Phys Sci, Callaghan, NSW 2308, Australia
[3] SUNY Binghamton, Dept Math Sci, POB 6000, Binghamton, NY 13902 USA
基金
英国工程与自然科学研究理事会;
关键词
D O I
10.1093/imrn/rny298
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The class S of totally disconnected locally compact (tdlc) groups that are non-discrete, compactly generated, and topologically simple contains many compelling examples. In recent years, a general theory for these groups, which studies the interaction between the compact open subgroups and the global structure, has emerged. In this article, we study the non-discrete tdlc groups H that admit a continuous embedding with dense image into some G is an element of S; that is, we consider the dense locally compact subgroups of groups G is an element of v. We identify a class R of almost simple groups that properly contains S and is moreover stable under passing to a non-discrete dense locally compact subgroup. We show that R enjoys many of the same properties previously obtained for S and establish various original results for R that are also new for the subclass S, notably concerning the structure of the local Sylow subgroups and the full automorphism group.
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页码:5037 / 5110
页数:74
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