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Covering monolithic groups with proper subgroups | ||
| International Journal of Group Theory | ||
| مقاله 11، دوره 2، شماره 1، خرداد 2013، صفحه 131-144 اصل مقاله (490.64 K) | ||
| نوع مقاله: Ischia Group Theory 2012 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2674 | ||
| نویسنده | ||
| Martino Garonzi* | ||
| University of Padova | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Covers؛ Monolithic groups؛ Primitive groups | ||
| مراجع | ||
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