What question did this study set out to answer?

The study aims to validate a conjecture regarding the correlation between Brauer characters and a group's normal subgroups.

February 19, 2026Journal of the London Mathematical Society0 citationsOpen Access

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Alperin's bound and normal Sylow subgroups

ZFZhicheng FengSouthern University of Science and Technology JMJ. Miquel MartínezUniversitat de València DRDamiano RossiRutgers, The State University of New Jersey

Key Points

The study aims to validate a conjecture regarding the correlation between Brauer characters and a group's normal subgroups.
Exploration of Alperin's lower bound in the context of Brauer characters.
Analysis of finite simple groups to connect with the conjecture.
Proof demonstration for the case of the prime 2.
Confirmed the conjecture for prime groups, establishing a connection to normal subgroups.
Proved a reduction theorem for blockwise Alperin's bound in finite groups of maximal defect.

Abstract

Abstract Let be a finite group, a prime number and a Sylow ‐subgroup of . Recently, Malle, Navarro, and Tiep conjectured that the number of ‐Brauer characters of coincides with that of the normalizer if and only if is normal in . We reduce this conjecture to a question about finite simple groups and prove it for the prime . As a by‐product of our work, we prove a reduction theorem for the blockwise version of Alperin's lower bound on ‐Brauer characters and prove it for 2‐blocks of maximal defect. This improves recent results obtained by Malle, Navarro, and Tiep.

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Cite This Study

Feng et al. (Sun,) studied this question.

synapsesocial.com/papers/6996a869ecb39a600b3ef26f https://doi.org/https://doi.org/10.1112/jlms.70470

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