We show that the principal p-block of a finite group of order divisible by p has at least 2\sqrt{p−1} height-zero characters. Along the way, we describe the p-local structure of finite groups whose principal p-blocks have at most five height-zero ordinary irreducible characters.
Height zero characters in principal blocks / Hung N.N.; Schaeffer Fry A.A.; Vallejo C.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 622:(2023), pp. 197-219. [10.1016/j.jalgebra.2023.01.021]
Height zero characters in principal blocks
Vallejo C.
2023
Abstract
We show that the principal p-block of a finite group of order divisible by p has at least 2\sqrt{p−1} height-zero characters. Along the way, we describe the p-local structure of finite groups whose principal p-blocks have at most five height-zero ordinary irreducible characters.
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