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  • SOME REMARKS ON GROUPS WITH NILPOTENT MINIMAL COVERS

  • Part of
  • R. A. BRYCE, L. SERENA
  • Journal:
    Journal of the Australian Mathematical Society / Volume 85 / Issue 3 / December 2008
    Published online by Cambridge University Press:
    01 December 2008, pp. 353-365
    Print publication:
    December 2008
    • Article
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  • 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.