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SUMMARY:Nguyen Ngoc Hung (University of Akron (USA))
DTSTART:20210312T162000Z
DTEND:20210312T170500Z
DTSTAMP:20260423T004133Z
UID:FGV/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGV/11/">Bou
 nding $p$-regular conjugacy classes and $p$-Brauer characters in finite gr
 oups</a>\nby Nguyen Ngoc Hung (University of Akron (USA)) as part of Finit
 e Groups in Valencia\n\n\nAbstract\nWe discuss two closely related problem
 s on bounding the number of $p$-regular conjugacy classes of a finite grou
 p $G$ and bounding the number of irreducible $p$-Brauer characters of $G$ 
 or a block of $G$. Among other results we will show that the number of $p$
 -regular classes of a finite group $G$ is bounded below by $2\\sqrt{p−1}
 +1−k_p(G)$\, where $k_p(G)$ is the number of classes of $p$-elements of 
 $G$. This and the celebrated Alperin weight conjecture imply the same boun
 d for the number of irreducible $p$-Brauer characters in the principal $p$
 -block of $G$. We also discuss the bounds in the minimal situation when $G
 $ has a unique class of nontrivial $p$-elements\, which have applications 
 to the study of principal blocks with few characters. The talk is based on
  joint works with A. Moretó\, with A. Maroti\, and with B. Sambale and P.
 H. Tiep.\n
LOCATION:https://researchseminars.org/talk/FGV/11/
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