covering monolithic groups with proper subgroups
نویسندگان
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 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.
منابع مشابه
Covering Monolithic Groups with Proper Subgroups
Given a finite non-cyclic group G, call σ(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 σ(G) < σ(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 stud...
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عنوان ژورنال:
international journal of group theoryناشر: university of isfahan
ISSN 2251-7650
دوره 2
شماره 1 2013
کلمات کلیدی
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