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 / R.D. Blyth; F. Fumagalli; M. Morigi. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 427:(2015), pp. 375-386. [10.1016/j.jalgebra.2014.12.033]
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.File in questo prodotto:
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