Work

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

Year: 2024

Type: article

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.

Source: Journal of Combinatorial Theory Series A

DOI: 10.1016/j.jcta.2024.105954

Authors: Attila Maróti, Juan Martínez, Alexander Moretó

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, Universitat de València

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450