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  • Finite dinilpotent groups of small derived length

  • Part of
  • John Cossey, Yanming Wang
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 67 / Issue 3 / December 1999
    Published online by Cambridge University Press:
    09 April 2009, pp. 318-328
    Print publication:
    December 1999
    • Article
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  • A finite dinilpotent group G is one that can be written as the product of two finite nilpotent groups, A and B say. A finite dinilpotent group is always soluble. If A is abelian and B is metabelian, with |A| and|B| coprime, we show that a bound on the derived length given by Kazarin can be improved. We show that G has derived length at most 3 unless G contains a section with a well defined structure: in particular if G is of odd order, G has derived length at most 3.