The solvability of groups with nilpotent minimal coverings
| Autor: | Francesco Fumagalli, Marta Morigi, Russell D. Blyth |
|---|---|
| Přispěvatelé: | R.D. Blyth, F. Fumagalli, M. Morigi |
| Rok vydání: | 2014 |
| Předmět: |
Finite group
Algebra and Number Theory group theory cover of a group almost simple groups Group (mathematics) Almost simple group Group Theory (math.GR) Combinatorics Nilpotent Mathematics::Group Theory Cardinality Simple (abstract algebra) 20D99 20E32 20D15 Cover of a group finite group FOS: Mathematics Minimal counterexample Finite set Mathematics - Group Theory Mathematics |
| DOI: | 10.48550/arxiv.1409.7501 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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