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SUMMARY:Quasirandom groups - Tim Gowers (Cambridge University)
DTSTART:20070227T170000Z
DTEND:20070227T180000Z
UID:TALK5748@talks.cam.ac.uk
CONTACT:Ben Green
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 cy
 clic group of size n contains a\nsum-free subset of size at least n/3\, an
 d this implies the same result for the product of a cyclic group with any 
 other finite group -- and hence for all finite Abelian groups. Babai and S
 os asked whether a similar result was true for finite groups in general: i
 s there a constant c>0 such that every group of order n contains a product
 -free subset of size at least cn? This talk will be about a property that 
 many finite groups have\, which is closely related to quasirandomness prop
 erties of graphs. It turns out that many natural families of groups\, incl
 uding all finite simple groups\, have this property\, and that no group wi
 th this property has a large product-free subset. Thus\, the question of B
 abai\nand Sos has a negative answer for a typical "natural"\nfinite non-Ab
 elian group.
LOCATION:MR4\, CMS
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