Publikationsdetails
Bounding p-Brauer characters in finite groups with two conjugacy classes of p-elements
- verfasst von
- Nguyen Ngoc Hung, Benjamin Sambale, Pham Huu Tiep
- Abstract
Let k(B_0) and l(B_0) respectively denote the number of ordinary and p-Brauer irreducible characters in the principal block B_0 of a finite group G. We prove that, if k(B_0)-l(B_0)=1, then l(B_0)\geq p-1 or else p=11 and l(B_0)=9. This follows from a more general result that for every finite group G in which all non-trivial p-elements are conjugate, l(B_0)\geq p-1 or else p = 11 and G/O_{p'}(G) =11^2:SL(2,5). These results are useful in the study of principal blocks with a few characters. We propose that, in every finite group G of order divisible by p, the number of irreducible Brauer characters in the principal p-block of G is always at least 2\sqrt{p-1}+1-k_p(G), where k_p(G) is the number of conjugacy classes of p-elements of G. This indeed is a consequence of the celebrated Alperin weight conjecture and known results on bounding the number of p-regular classes in finite groups.
- Organisationseinheit(en)
-
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
- Externe Organisation(en)
-
University of Akron
Rutgers University
- Typ
- Artikel
- Journal
- Israel Journal of Mathematics
- Band
- 262
- Seiten
- 327–358
- ISSN
- 0021-2172
- Publikationsdatum
- 09.2024
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- Elektronische Version(en)
-
http://arxiv.org/abs/2102.04443v2 (Zugang:
Offen)
https://doi.org/10.1007/s11856-024-2613-1 (Zugang: Offen)