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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Approximating simple locally compact groups by the
ir dense subgroups - Phillip Wesolek (Binghamton U
niversity)
DTSTART;TZID=Europe/London:20170511T113000
DTEND;TZID=Europe/London:20170511T123000
UID:TALK72498AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72498
DESCRIPTION:Co-authors: Pierre-Emmanuel Caprace (Universit&ea
cute\; catholique de Louvain)\, Colin Reid (Unive
rsity of Newcastle\, Australia ) \;The
collection of topologically simple totally disconn
ected locally compact (t.d.l.c.) groups which are
compactly generated and non-discrete\, denoted by
\, forms a rich and compelling c
lass of locally compact groups. Members of this cl
ass include the simple algebraic groups over non-a
rchimedean local fields\, the tree almost automorp
hism groups\, and groups acting on cu
be complexes.

\;In this talk\, we stud
y the non-discrete t.d.l.c. groups
which admit a continuous embedding with dense ima
ge into some group \;\; that is\, we st
udy the non-discrete t.d.l.c. groups which approxi
mate \;groups \; \;. We consider
a class which contains all suc
h t.d.l.c. groups and show enj
oys many of the same properties previously establi
shed for . Using these more gene
ral 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 t
here is a finite set of primes suc
h that every compact subgroup of is vi
rtually pro- .
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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