Alperin's bound and normal Sylow subgroups
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.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Algebra and Geometry
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 113
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN