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EnglishA 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.
| Titolo: | The solvability of groups with nilpotent minimal coverings |
| Autore/i: | R. D. Blyth; F. Fumagalli; MORIGI, MARTA |
| Autore/i Unibo: | |
| Anno: | 2015 |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jalgebra.2014.12.033 |
| 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. |
| Data stato definitivo: | 2015-09-25T10:48:31Z |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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Utilizza questo identificativo per citare o creare un link a questo documento:
http://hdl.handle.net/11585/495167
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