%0 Journal Article
%T Covering monolithic groups with proper subgroups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Garonzi, Martino
%D 2013
%\ 03/01/2013
%V 2
%N 1
%P 131-144
%! Covering monolithic groups with proper subgroups
%K Covers
%K Monolithic groups
%K Primitive groups
%R 10.22108/ijgt.2013.2674
%X Given a finite non-cyclic group $G$, call $\sigma(G)$ the smallest number of proper subgroups of $G$ needed to cover $G$. Lucchini and Detomi conjectured that if a nonabelian group $G$ is such that $\sigma(G) < \sigma(G/N)$ for every non-trivial normal subgroup $N$ of $G$ then $G$ is monolithic, meaning that it admits a unique minimal normal subgroup. In this paper we show how this conjecture can be attacked by the direct study of monolithic groups.
%U https://ijgt.ui.ac.ir/article_2674_ea33a8a83df38a9fbe3ccb5bf483e473.pdf