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SUMMARY:The width of a group - Nick Gill (Open University)
DTSTART:20121128T143000Z
DTEND:20121128T150000Z
UID:TALK40741@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:I describe recent work with Pyber\, Short and Szabo in which w
 e study the\n`width' of a finite simple group. Given a group G and a subse
 t A of G\, the\n`width of G with respect to A' - w(G\,A) - is the 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\nLiebeck\, Nikolov and Shalev have con
 jectured that in this 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 th
 is conjecture as well as describing some\ninteresting\, and unexpected\, c
 onnections between this work and classical\nadditive combinatorics. In par
 ticular the notion of a normal K-approximate\ngroup will be introduced.
LOCATION:MR11\, CMS
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