Sylow subgroups and the number of irreducible characters of degrees divisible by a prime p
Abstract Let be a finite group and be a prime. We establish an upper bound for the derived length of a Sylow ‐subgroup of in terms of the number of irreducible characters of whose degrees are divisible by . We also prove that if is a ‐block of a finite ‐solvable group with defect group , then the derived length of is at most one more than the number of ordinary irreducible characters of positive height in .
Authors
- Mark L. Lewis (ORCID: https://orcid.org/0000-0001-9627-6922)
- A. A. Schaeffer Fry (ORCID: https://orcid.org/0000-0002-1690-9046)
- Hung P. Tong‐Viet (ORCID: https://orcid.org/0000-0001-7545-4945)
- James P. Cossey
Institutions
- University of Akron (US)
- Binghamton University (US)
- University of Denver (US)
- Kent State University (US)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2026-06-26
- DOI
- https://doi.org/10.1112/blms.70428
- Primary Topic
- Finite Group Theory Research
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00