On minimal coverings and pairwise generation of some primitive groups of wreath product type
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Published:2023-05-30
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Volume:
Page:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Almeida Júlia1,
Garonzi Martino1ORCID
Affiliation:
1. Departamento de Matemática, Universidade de Brasília, Campus Universitário Darcy Ribeiro, Brasília-DF, 70910-900, Brazil
Abstract
The covering number of a finite group [Formula: see text], denoted [Formula: see text], is the smallest positive integer [Formula: see text] such that [Formula: see text] is a union of [Formula: see text] proper subgroups. We calculate [Formula: see text] for a family of primitive groups [Formula: see text] with a unique minimal normal subgroup [Formula: see text], isomorphic to [Formula: see text] with [Formula: see text] divisible by [Formula: see text] and [Formula: see text] cyclic. This is a generalization of a result of Swartz concerning the symmetric groups. We also prove an asymptotic result concerning pairwise generation.
Funder
Conselho Nacional de Desenvolvimento Cientifico e Tecnologico
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory