Work

Alperin's bound and normal Sylow subgroups

Year: 2026

Type: article

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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70470

Authors: Zhicheng Feng, J. Miquel Martínez, Damiano Rossi

Institutions: Southern University of Science and Technology, Universitat de València, Rutgers, The State University of New Jersey

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: European Commission, Deutsche Forschungsgemeinschaft, National Natural Science Foundation of China, Ministerio de Ciencia e Innovación