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Covering the set of p-elements in finite groups by proper subgroups.
- Source :
-
Journal of Combinatorial Theory - Series A . Feb2025, Vol. 210, pN.PAG-N.PAG. 1p. - Publication Year :
- 2025
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SOLVABLE groups
Subjects
Details
- Language :
- English
- ISSN :
- 00973165
- Volume :
- 210
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series A
- Publication Type :
- Academic Journal
- Accession number :
- 181092110
- Full Text :
- https://doi.org/10.1016/j.jcta.2024.105954