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SUMMARY:Equations in Periodic Groups
DTSTART;VALUE=DATE-TIME:20211213T150000Z
DTEND;VALUE=DATE-TIME:20211213T161500Z
DTSTAMP;VALUE=DATE-TIME:20220123T221644Z
UID:indico-event-7255@indico.math.cnrs.fr
DESCRIPTION:\n The free Burnside group B(r\,n) is the quotient of the free
group of rank r by the normal subgroup generated by the n-th power of all
its elements. It was introduced in 1902 by Burnside\, who asked whether B
(r\,n) is necessarily a finite group or not. In 1968 Novikov and Adian pro
ved 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 structur
e. In this talk we are interested in understanding equations in B(r\,n). I
n particular we want to investigate the following problem: given a set of
equations S\, under which conditions does every solution to S in B(r\,n) a
lready come from a solution in the free group of rank r?\n Along the way w
e will explore other aspects of certain periodic groups (i.e. quotients of
a free Burnside group) such as the Hopf / co-Hopf property\, the isomorph
ism problem\, their automorphism groups\, etc.\n Joint work with Z. Sela.\
n\n\n==================================================================\n\
nIHES Covid-19 regulations:\n\n- all the participants who will attend the
event in person will have to keep their mask on in indoor spaces\nand wher
e the social distancing is not possible\;\n- speakers will be free to wear
their mask or not at the moment of their talk if they feel more comfortab
le\nwithout it\;\n- Up to 70 persons in the conference room\, every partic
ipant will be asked to be able to provide a health pass\n- Over 70 persons
in the conference room\, every participant will be asked to provide a hea
lth pass which will\nbe checked at the entrance of the conference room.\n\
n==================================================================\n\nhtt
ps://indico.math.cnrs.fr/event/7255/
LOCATION:IHES Centre de confĂ©rences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/7255/
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