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Research Report MRR98-029

Finite dinilpotent groups of small derived length

John Cossey and Yanming Wang

Abstract: A finite dinilpotent grouup 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 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.

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