Maximal covers of finite groups

Igor Lima; Raimundo Bastos; José R. Rogério

doi:10.1080/00927872.2019.1654498

Maximal covers of finite groups

Group Theory 2020-03-16 v1

Authors: Igor Lima , Raimundo Bastos , José R. Rogério

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Abstract

Let $\lambda(G)$ be the maximum number of subgroups in an irredundant covering of the finite group $G$ . We prove that if $G$ is a group with $\lambda(G) \leqslant 6$ , then $G$ is supersolvable. We also describe the structure of the groups $G$ with $\lambda(G)=6$ . Moreover, we show that if $G$ is a group with $\lambda(G) \leqslant 30$ , then $G$ is solvable.

Keywords

finite groups irredundant covering supersolvable groups solvable groups group theory

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@article{arxiv.1804.05390,
  title  = {Maximal covers of finite groups},
  author = {Igor Lima and Raimundo Bastos and José R. Rogério},
  journal= {arXiv preprint arXiv:1804.05390},
  year   = {2020}
}

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Submitted to an internacional journal

Maximal covers of finite groups

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