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SUMMARY:Equations in periodic groups  - Remi Coulon (University of Rennes)
DTSTART:20220211T134500Z
DTEND:20220211T144500Z
UID:TALK169784@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:The free Burnside group B(r\,n) is the quotient of the free gr
 oup of rank r by the normal subgroup generated by the n-th power of all it
 s elements.\nIt was introduced in 1902 by Burnside who asked whether B(r\,
 n) is necessarily a finite group or not. In 1968 Novikov and Adian proved 
 that if r > 1 and n is a sufficiently large odd exponent\, then B(r\,n) is
  actually infinite. It turns out that B(r\,n) has a very rich structure. I
 n this talk we are interested in understanding equations in B(r\,n). In pa
 rticular we want to investigate the following problem. Given a set of equa
 tions S\, under which conditions\, every solution to S in B(r\,n) already 
 comes from a solution in the free group of rank r.\n\nAlong the way we wil
 l explore other aspects of certain periodic groups (i.e. quotients of a fr
 ee Burnside groups) such that the Hopf / co-Hopf property\, the isomorphis
 m problem\, their automorphism groups\, etc.\n\nJoint work with Z. Sela\n\
 n
LOCATION:Zoom
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