Garonzi, M. (2013). Covering monolithic groups with proper subgroups. International Journal of Group Theory, 2(1), 131-144. doi: 10.22108/ijgt.2013.2674

Martino Garonzi. "Covering monolithic groups with proper subgroups". International Journal of Group Theory, 2, 1, 2013, 131-144. doi: 10.22108/ijgt.2013.2674

Garonzi, M. (2013). 'Covering monolithic groups with proper subgroups', International Journal of Group Theory, 2(1), pp. 131-144. doi: 10.22108/ijgt.2013.2674

Garonzi, M. Covering monolithic groups with proper subgroups. International Journal of Group Theory, 2013; 2(1): 131-144. doi: 10.22108/ijgt.2013.2674

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.

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