Fixed‐point ratios, Sylow numbers, and coverings of p$p$‐elements in finite groups
Abstract Fixed‐point ratios for primitive permutation groups have been extensively studied. Relying on a recent work of Burness and Guralnick, we obtain further results in the area. For a prime and a finite group , we use fixed‐point ratios to study the number of Sylow ‐subgroups of and the minimal size of a covering by proper subgroups of the set of ‐elements of .
Authors
- Attila Maróti (ORCID: https://orcid.org/0000-0002-6896-3378)
- Noelia Rizo (ORCID: https://orcid.org/0000-0002-5497-6151)
- Alexander Moretó (ORCID: https://orcid.org/0000-0002-6914-9650)
- Juan José Prieto Martínez (ORCID: https://orcid.org/0000-0003-4954-1599)
- Robert M. Guralnick (ORCID: https://orcid.org/0000-0002-9094-857X)
Institutions
- University of Southern California (US)
- HUN-REN Alfréd Rényi Institute of Mathematics (HU)
- Universitat de València (ES)
Publication Details
- Journal
- Journal of the London Mathematical Society
- Published
- 2025-05-01
- DOI
- https://doi.org/10.1112/jlms.70167
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Generalitat Valenciana
- Ministerio de Ciencia e Innovación
- National Research, Development and Innovation Office