Irredundant and minimal covers of finite groups

Andrea Lucchini; Martino Garonzi

Irredundant and minimal covers of finite groups

Group Theory 2014-12-22 v1

Authors: Andrea Lucchini , Martino Garonzi

Abstract

A cover of a finite non-cyclic group $G$ is a family $\mathcal{H}$ of proper subgroups of $G$ whose union equals $G$ . A cover of $G$ is called minimal if it has minimal size, and irredundant if it does not properly contain any other cover. We classify the finite non-cyclic groups all of whose irredundant covers are minimal.

Keywords

finite groups group covers irredundant covers minimal covers non-cyclic groups proper subgroups classification

Cite

@article{arxiv.1412.6275,
  title  = {Irredundant and minimal covers of finite groups},
  author = {Andrea Lucchini and Martino Garonzi},
  journal= {arXiv preprint arXiv:1412.6275},
  year   = {2014}
}

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