%0 Journal Article
%T Covering monolithic groups with proper subgroups
%A Martino Garonzi
%J International Journal of Group Theory
%D 2013
%I University of Isfahan
%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 textit{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.
%K Covers
%K Monolithic groups
%K Primitive groups
%U http://www.theoryofgroups.ir/?_action=showPDF&article=2674&_ob=ea33a8a83df38a9fbe3ccb5bf483e473&fileName=full_text.pdf.