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arXiv · 1409.7501

The solvability of groups with nilpotent minimal coverings

Russell D. Blyth·Francesco Fumagalli·Marta Morigi
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Abstract

A covering of a group is a finite set of proper subgroups whose union is the whole group. A covering is minimal if there is no covering of smaller cardinality, and it is nilpotent if all its members are nilpotent subgroups. We complete a proof that every group that has a nilpotent minimal covering is solvable, starting from the previously known result that a minimal counterexample is an almost simple finite group.

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Russell D. Blyth, Francesco Fumagalli, Marta Morigi. 2014-09-26. The solvability of groups with nilpotent minimal coverings. https://arxiv.org/abs/1409.7501

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