solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看200次
Approximating simple locally compact groups by their dense locally compact subgroups. (arXiv:1706.07317v1 [math.GR])
来源于:arXiv
The class, denoted by $\mathscr{S}$, of totally disconnected locally compact
groups which 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
totally disconnected locally compact groups $H$ that admit a continuous
embedding with dense image into some $G\in \mathscr{S}$; that is, we consider
the dense locally compact subgroups of groups $G\in \mathscr{S}$. We identify a
class $\mathscr{R}$ of almost simple groups which properly contains
$\mathscr{S}$ and is moreover stable under passing to a non-discrete dense
locally compact subgroup. We show that $\mathscr{R}$ enjoys many of the same
properties previously obtained for $\mathscr{S}$ and establish various original
results for $\mathscr{R}$ that are also new for the subclass $\mathscr{S}$,
notabl 查看全文>>