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Finite dinilpotent groups of small derived length

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

John Cossey  and
Yanming Wang
John Cossey
Affiliation:
Mathematics Department School of Mathematical Sciences Australian National UniversityCanberra 0200Australia e-mail: john.cossey@maths.anu.edu.au
Yanming Wang
Affiliation:
Department of Mathematics Zhongshan University of Guangzhou510275 P. R.China e-mail: stswym@zsulink.zsu.edu.cn
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Abstract

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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.

Keywords

finite soluble groupsdinilpotent groupsderived length

MSC classification

Secondary: 20D60: Arithmetic and combinatorial problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 3 , December 1999 , pp. 318 - 328
Copyright
Copyright © Australian Mathematical Society 1999

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