BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Approximating simple locally compact groups by their dense subgrou ps - Phillip Wesolek (Binghamton University) DTSTART:20170511T103000Z DTEND:20170511T113000Z UID:TALK72498@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:Co-authors: Pierre-Emmanuel Caprace (Université\; catho lique de Louvain)\, Colin Reid (University of Newcastle\, Australia ) \;The collection of topologically simple totally disconnected loca lly compact (t.d.l.c.) groups which are compactly generated and non-discre te\, denoted by

\, forms a ric h and compelling class of locally compact groups. Members of this class in clude the simple algebraic groups over non-archimedean local fields\, the tree almost automorphism groups\, and groups acting on

< img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML- CSS/TeX/png/Main/Regular/141/0054.png">

cube complexes.

\;In this talk\, w e study the non-discrete t.d.l.c. groups

which admit a continuous embedding with dense image into some gro up

\;\; t hat 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 establi shed for

. Using these more ge neral results\, new restrictions on the members of

are obtained. For any

\, we prove that any infinite Sylow pro-< img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML- CSS/TeX/png/Math/Italic/141/0070.png"> subgroup of a compact open subgro up of

is not solvable. We prove further that there is a finite set of primes

such that every compact subgroup of

is virtually pro-

. LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR