Abstract
We generalize Murai's conjecture on an upper bound for the number of irreducible $p$-Brauer characters in the principal block to an arbitrary block. We prove that the new conjecture has an affirmative answer for tame blocks and blocks with cyclic defect groups. In addition we confirm Murai's conjecture for symmetric and alternating groups.
Acknowledgments
We are deeply grateful to the referee for his/her invaluable comments. The first and second authors were supported by National Key R&D Program of China (Grant No. 2020YFE0204200), NSFC (12171211) and the Natural Science Foundation of Jiangxi Province (20192ACB21008), and the third author was supported by NSFC (12201155).
Citation
Yanjun Liu. Wolfgang Willems. Huan Xiong. "A generalization of Murai's conjecture." Osaka J. Math. 61 (1) 107 - 119, January 2024.
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