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SUMMARY:Emanuele Pacifici (Università degli Studi di Milano (Italy))
DTSTART:20210330T133000Z
DTEND:20210330T141500Z
DTSTAMP:20260423T004132Z
UID:FGV/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGV/22/">On 
 Huppert’s $\\rho-\\sigma$ conjecture</a>\nby Emanuele Pacifici (Universi
 tà degli Studi di Milano (Italy)) as part of Finite Groups in Valencia\n\
 n\nAbstract\nThe set of the degrees of the irreducible complex characters 
 of a finite group $G$ has been an object of considerable interest since th
 e second part of the 20th century\, and the study of the arithmetical stru
 cture of this set is a particularly intriguing aspect of Character Theory 
 of finite groups. A remarkable question in this research area was posed by
  B. Huppert in the 80’s: is it true that at least one of the character d
 egrees is divisible by a ”large” portion of the entire set of primes t
 hat appear as divisors of some character degree? More precisely\, denoting
  by $\\rho(G)$ the set of primes that divide some character degree\, and b
 y $\\sigma(G)$ the largest number of primes that divide a single character
  degree\, Huppert’s $\\rho-\\sigma$ conjecture predicts that $|\\rho(G)|
  ≤ 3\\sigma(G)$ holds for every finite group G\, and that $|\\rho(G)| 
 ≤ 2\\sigma(G)$ if $G$ is solvable. In this talk we will discuss some rec
 ent developments in the study of Huppert’s conjecture\, obtained in a jo
 int work with Z. Akhlaghi and S. Dolfi.\n
LOCATION:https://researchseminars.org/talk/FGV/22/
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