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SUMMARY:Noelia Rizo (Universitat de València (Spain))
DTSTART:20210316T152000Z
DTEND:20210316T154500Z
DTSTAMP:20260423T004132Z
UID:FGV/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGV/17/">Cou
 nting characters in blocks</a>\nby Noelia Rizo (Universitat de València (
 Spain)) as part of Finite Groups in Valencia\n\n\nAbstract\nLet $G$ be a f
 inite group\, let $p$ be a prime number and let $B$ be a $p$-block of $G$ 
 with defect group $D$. Studying the structure of $D$ by means of the knowl
 edge of some aspects of $B$ is a main area in character theory of finite g
 roups. Let $k(B)$ be the number of irreducible characters in the $p$-block
  $B$. It is well-known that $k(B)=1$ if\, and only if\, $D$ is trivial. It
  is also true that $k(B)=2$ if\, and only if\, $|D|=2$. For blocks $B$ wit
 h $k(B)=3$ it is conjectured that $|D|=3$. \n\nIn this talk we restrict ou
 r attention to the principal $p$-block of $G$\, $B_0(G)$\, that is\, the $
 p$-block containing the trivial character of $G$. In this case\, by work o
 f Belonogov\, Koshitani and Sakurai we know the structure of $D$ when $k(B
 _0(G))=3$ or $4$. In this work\, we go one step further and analyze the st
 ructure of D when $k(B_0(G))=5$. \n\nThis is a joint work with Mandi Schae
 ffer Fry and Carolina Vallejo.\n
LOCATION:https://researchseminars.org/talk/FGV/17/
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