Covering the set of p-elements in finite groups by proper subgroups
Let p be a prime and let G be a finite group which is generated by the set G p of its p -elements. We show that if G is solvable and not a p -group, then the minimal number σ p ( G ) of proper subgroups of G whose union contains G p is equal to 1 less than the minimal number of proper subgroups of G whose union is G . For p -solvable groups G , we always have σ p ( G ) ≥ p + 1 . We study the case of alternating and symmetric groups G in detail.
Authors
- Attila Maróti (ORCID: https://orcid.org/0000-0002-6896-3378)
- Alexander Moretó (ORCID: https://orcid.org/0000-0002-6914-9650)
- Juan José Prieto Martínez (ORCID: https://orcid.org/0000-0003-4954-1599)
Institutions
- HUN-REN Alfréd Rényi Institute of Mathematics (HU)
- Universitat de València (ES)
Publication Details
- Journal
- Journal of Combinatorial Theory Series A
- Published
- 2024-09-20
- DOI
- https://doi.org/10.1016/j.jcta.2024.105954
- Citations
- 1
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 1.32
Funders
- Ministerio de Ciencia e Innovación
- Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
- European Research Council
- Horizon 2020
- H2020 European Research Council