University of IsfahanInternational Journal of Group Theory2251-76502120130301Covering monolithic groups with proper subgroups131144267410.22108/ijgt.2013.2674ENMartinoGaronziUniversity of PadovaJournal Article20121230Given 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 <em>monolithic</em>, 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.https://ijgt.ui.ac.ir/article_2674_ea33a8a83df38a9fbe3ccb5bf483e473.pdf