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.

The solvability of groups with nilpotent minimal coverings

MORIGI, MARTA
2015

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.
R.D. Blyth; F. Fumagalli; M. Morigi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/495167
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