Presented by:
Phillip Wesolek
Date:
Thursday 11th May 2017 - 11:30 to 12:30
Venue:
INI Seminar Room 1
Abstract:
Co-authors: Pierre-Emmanuel Caprace (Université catholique de Louvain), Colin Reid (University of Newcastle, Australia ) The collection of topologically simple totally disconnected locally compact (t.d.l.c.) groups which are compactly generated and non-discrete, denoted by 
, forms a rich and compelling class of locally compact groups. Members of this class include the simple algebraic groups over non-archimedean local fields, the tree almost automorphism groups, and groups acting on 
cube complexes.
In this talk, we study the non-discrete t.d.l.c. groups
which admit a continuous embedding with dense image into some group 
; that is, we study the non-discrete t.d.l.c. groups which approximate groups . We consider a class 
which contains all such t.d.l.c. groups and show
enjoys many of the same properties previously established for
. Using these more general results, new restrictions on the members of
are obtained. For any
, we prove that any infinite Sylow pro-
subgroup of a compact open subgroup of
is not solvable. We prove further that there is a finite set of primes 
such that every compact subgroup of 
is virtually pro-
.
, forms a rich and compelling class of locally compact groups. Members of this class include the simple algebraic groups over non-archimedean local fields, the tree almost automorphism groups, and groups acting on
cube complexes.In this talk, we study the non-discrete t.d.l.c. groups
which admit a continuous embedding with dense image into some group ; that is, we study the non-discrete t.d.l.c. groups which approximate groups . We consider a class
which contains all such t.d.l.c. groups and show
enjoys many of the same properties previously established for
. Using these more general results, new restrictions on the members of
are obtained. For any
, we prove that any infinite Sylow pro-
subgroup of a compact open subgroup of
is not solvable. We prove further that there is a finite set of primes
such that every compact subgroup of
is virtually pro-
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