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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Quasirandom groups - Tim Gowers (Cambridge Univers
ity)
DTSTART;TZID=Europe/London:20070227T170000
DTEND;TZID=Europe/London:20070227T180000
UID:TALK5748AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/5748
DESCRIPTION:A subset of an Abelian group is called sum-free if
it contains no three elements x\,y\,z such that x
+y=z. It is\neasy to prove that a cyclic group of
size n contains a\nsum-free subset of size at leas
t n/3\, and this implies the same result for the p
roduct of a cyclic group with any other finite gro
up -- and hence for all finite Abelian groups. Bab
ai and Sos asked whether a similar result was true
for finite groups in general: is there a constant
c>0 such that every group of order n contains a p
roduct-free subset of size at least cn? This talk
will be about a property that many finite groups h
ave\, which is closely related to quasirandomness
properties of graphs. It turns out that many natur
al families of groups\, including all finite simpl
e groups\, have this property\, and that no group
with this property has a large product-free subset
. Thus\, the question of Babai\nand Sos has a nega
tive answer for a typical "natural"\nfinite non-Ab
elian group.
LOCATION:MR4\, CMS
CONTACT:Ben Green
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