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Covering the set of p-elements in finite groups by proper subgroups.

Authors :
Maróti, Attila
Martínez, Juan
Moretó, Alexander
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

Subjects :
*SOLVABLE groups

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