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• W2041226948 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/ $. 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.
• W2041226948 created "2016-06-24" @default.
• W2041226948 creator A5066540439 @default.
• W2041226948 date "2014-12-22" @default.
• W2041226948 modified "2023-09-27" @default.
• W2041226948 title "Cartan matrices and Brauer's k(B)-Conjecture IV" @default.
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• W2041226948 hasPublicationYear "2014" @default.
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