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SUMMARY:Small doubling in a free group - Imre Ruzsa (Renyi Institute for M
 athematics\, Hungarian Academy of Sciences)
DTSTART:20240412T103000Z
DTEND:20240412T113000Z
UID:TALK214039@talks.cam.ac.uk
DESCRIPTION:Let $A$ be a finite set in a free group\, $|A| =n$. If $|A+A| 
 = o(n^{3/2})$\, thenall but $o(n)$ elements of $A$ lie in a cyclic subgrou
 p. The exponent 3/2is best possible.\nUnlike the commutative case\, no suc
 h structural result follows from an estimateon the difference set $A-A$. H
 owever\, if both difference sets $A-A$ and $-A+A$have size $O(n^{9/8})$\, 
 then a similar conclusion follows. This exponent is probablynot optimal.
LOCATION:Seminar Room 1\, Newton Institute
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