Abstract: A cover of a group is a finite collection of proper subgroups whose union is the whole group. A cover is minimal if no cover of the group has fewer members. It is conjectured that a group with a minimal cover of nilpotent subgroups is soluble. It is shown that a minimal counterexample to this conjecture is almost simple and that none of a range of almost simple groups are counterexamples to the conjecture.
Some remarks on groups with nilpotent minimal covers / R.A. Bryce; L. Serena. - In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 1446-7887. - STAMPA. - 85:(2008), pp. 353-365. [10.1017/S1446788708000670]
Some remarks on groups with nilpotent minimal covers
SERENA, LUIGI
2008
Abstract
Abstract: A cover of a group is a finite collection of proper subgroups whose union is the whole group. A cover is minimal if no cover of the group has fewer members. It is conjectured that a group with a minimal cover of nilpotent subgroups is soluble. It is shown that a minimal counterexample to this conjecture is almost simple and that none of a range of almost simple groups are counterexamples to the conjecture.File | Dimensione | Formato | |
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