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SUMMARY:Products of conjugacy classes in finite groups - Carmen Melchor\, 
 Universidat Jaume I de Castelló
DTSTART:20171117T150000Z
DTEND:20171117T160000Z
UID:TALK94492@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:One of the most relevant problems about the structure of a fin
 ite group focused on the product of its conjugacy classes was posed in 198
 5 by Z. Arad and M. Herzog. They conjectured that in a non-abelian simple 
 group\, the product of two non-trivial classes can never be a single conju
 gacy class. The conjecture has been solved for several families of simple 
 groups. We will show new results about the product of conjugacy classes re
 garding the non-simplicity and the normal structure of a finite group G.\n
 \nSuppose that K is a conjugacy class of G. We know that KK^−1^ is alway
 s a G-invariant set\, so we can write KK^−1 ^ = 1 ∪ A\, where A is the
  join of conjugacy classes of G. When KK^−1^ = 1 ∪ D or KK^−1^ = 1 
 ∪ D ∪ D^−1^\, where D is a conjugacy class\, we prove that G is not 
 a non-abelian simple group by means of the Classification of the Finite Si
 mple Groups (CFSG). When K is real\, we also study the extreme case in whi
 ch A is a single class.\n\n(Joint work with Antonio Beltran and Maria Jos
 é Felipe)
LOCATION:CMS\, MR14
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