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• W3131036794 startingPage "1127" @default.
• W3131036794 abstract "We prove that the number of irreducible ordinary characters in the principal $p$-block of a finite group $G$ of order divisible by $p$ is always at least $2sqrt{p-1}$. This confirms a conjecture of H'{e}thelyi and K{u}lshammer for principal blocks and provides an affirmative answer to Brauer's Problem 21 for principal blocks of bounded defect. Our proof relies on recent works of Mar'{o}ti and Malle-Mar'{o}ti on bounding the conjugacy class number and the number of $p'$-degree irreducible characters of finite groups, earlier works of Brou'{e}-Malle-Michel and Cabanes-Enguehard on the distribution of characters into unipotent blocks and $e$-Harish-Chandra series of finite reductive groups, and known cases of the Alperin-McKay conjecture." @default.
• W3131036794 created "2021-03-01" @default.
• W3131036794 creator A5012113316 @default.
• W3131036794 creator A5037121524 @default.
• W3131036794 date "2023-05-26" @default.
• W3131036794 modified "2023-09-25" @default.
• W3131036794 title "On Héthelyi–Külshammer’s conjecture for principal blocks" @default.
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• W3131036794 doi "https://doi.org/10.2140/ant.2023.17.1127" @default.
• W3131036794 hasPublicationYear "2023" @default.
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