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SUMMARY:The Wiegold Conjecture for the Small Ree Groups
DTSTART:20260507T070000Z
DTEND:20260507T090000Z
DTSTAMP:20260501T164600Z
UID:indico-event-16119@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sira Busch\n\nLet G be a finite simple group and n 
 ≥ 3. Is the action of Aut(F_n) on Epi(F_n\, G) transitive? Research on t
 his question dates back to 1977\, and a positive answer is related to the 
 so-called Wiegold conjecture.For a prime number p\, a positive answer is k
 nown for the following groups:PSL(2\, p)\,Sz(2^{2m−1}) and PSL(2\, 2^m)\
 , for m ≥ 2\,PSL(2\, 3^p)\,PSL(2\, p^r)\, for r in N and n ≥ 4\,Alt(k)
 \, for k ≤ 11 and n = 3.We showed that it can also be answered positivel
 y for the small Ree groups ^2G_2 (3^{2e+1})\, for all e ≥ 1 and all n 
 ≥ 5. This was joint work with Mark Pengitore\, Jeroen Schillewaert and H
 endrik Van Maldeghem.In this talk\, we provide some insight into the conje
 cture\, discuss some of the methods used to prove our result for the small
  Ree groups\, and explain why it is not easy to resolve all cases.\n\nhttp
 s://indico.math.cnrs.fr/event/16119/
LOCATION:112 (Braconnier)
URL:https://indico.math.cnrs.fr/event/16119/
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