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SUMMARY:Nicola Grittini (Università degli Studi  di Firenze (Italy))
DTSTART:20210312T152000Z
DTEND:20210312T154500Z
DTSTAMP:20260423T004658Z
UID:FGV/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGV/10/">The
  generalization of a theorem on real valued characters</a>\nby Nicola Grit
 tini (Università degli Studi  di Firenze (Italy)) as part of Finite Group
 s in Valencia\n\n\nAbstract\nThe Theorem of Ito-Michler\, one of the most 
 celebrated results in character theory of finite groups\, states that a gr
 oup has a normal abelian Sylow $p$-subgroup if and only if the prime numbe
 r $p$ does not divide the degree of any irreducible character of the group
 .\n\nAmong the many variants of the theorem\, there exists one\, due to Do
 lfi\, Navarro and Tiep\, which involves only the real valued irreducible c
 haracters of the group\, and the prime number $p = 2$.\n\nThis variant\, h
 owever\, fails if we consider a prime number different from 2\, and any ge
 neralization in this direction seems hard\, due to some specific propertie
 s of real valued characters.\n\nThis talk proposes a new way to approach t
 he problem\, which takes into account a different subset of the irreducibl
 e characters\, however related with real valued characters. This new appro
 ach has already been partially successful and it may suggest a way to gene
 ralize also other similar results.\n
LOCATION:https://researchseminars.org/talk/FGV/10/
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