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Covering monolithic groups with proper subgroups
Given a finite non-cyclic group , call the smallest number of
proper subgroups of needed to cover . Lucchini and Detomi conjectured
that if a nonabelian group is such that for every
non-trivial normal subgroup of then 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.Comment: I wrote this paper for the Proceedings of the conference "Ischia
Group Theory 2012" (March, 26th - 29th 2012
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