Covering Certain Monolithic Groups with Proper Subgroups
نویسندگان
چکیده
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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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 thi...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2013
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2011.622325