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CATEGORIES:Discrete Analysis Seminar
SUMMARY:The width of a group - Nick Gill (Open University)
DTSTART;TZID=Europe/London:20121128T143000
DTEND;TZID=Europe/London:20121128T150000
UID:TALK40741AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/40741
DESCRIPTION:I describe recent work with Pyber\, Short and Szab
o in which we study the\n`width' of a finite simpl
e group. Given a group G and a subset A of G\, the
\n`width of G with respect to A' - w(G\,A) - is th
e smallest number k such that G\ncan be written as
the product of k conjugates of A. If G is finite
and simple\,\nand A is a set of size at least 2\,
then w(G\,A) is well-defined\; what is more\nLiebe
ck\, Nikolov and Shalev have conjectured that in t
his situation there\nexists an absolute constant c
such that w(G\,A)\\leq c log|G|/log|A|.\n\nI will
present a partial proof of this conjecture as wel
l as describing some\ninteresting\, and unexpected
\, connections between this work and classical\nad
ditive combinatorics. In particular the notion of
a normal K-approximate\ngroup will be introduced.
LOCATION:MR11\, CMS
CONTACT:Ben Green
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