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- W4299924517 abstract "For a block $B$ of a finite group we prove that $k(B)le(det C-1)/l(B)+l(B)ledet C$ where $k(B)$ (respectively $l(B)$) is the number of irreducible ordinary (respectively Brauer) characters of $B$, and $C$ is the Cartan matrix of $B$. As an application, we show that Brauer's $k(B)$-Conjecture holds for every block with abelian defect group $D$ and inertial quotient $T$ provided there exists an element $uin D$ such that $C_T(u)$ acts freely on $D/<u>$. This gives a new proof of Brauer's Conjecture for abelian defect groups of rank at most $2$. We also prove the conjecture in case $l(B)le 3$." @default.
- W4299924517 created "2022-10-03" @default.
- W4299924517 creator A5066540439 @default.
- W4299924517 date "2014-12-22" @default.
- W4299924517 modified "2023-10-18" @default.
- W4299924517 title "Cartan matrices and Brauer's k(B)-Conjecture III" @default.
- W4299924517 doi "https://doi.org/10.48550/arxiv.1412.7017" @default.
- W4299924517 hasPublicationYear "2014" @default.
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