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Groups of odd order in which every subnormal subgroup has defect at most two

Part of: Representation theory of groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

John Cossey
John Cossey
Affiliation:
Department of Mathematics A.N.U. GPO Box 4 Canberra, ACT 2601, Australia
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Abstract

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In 1980, McCaughan and Stonehewer showed that a finite soluble group in which every subnormal subgroup has defect at most two has derived length at most nine and Fitting length at most five, and gave an example of derived length five and Fitting length four. In 1984 Casolo showed that derived length five and Fitting length four are best possible bounds.

In this paper we show that for groups of odd order the bounds can be improved. A group of odd order with every subnormal subgroup of defect at most two has derived and Fitting length at most three, and these bounds are best possible.

MSC classification

Secondary: 20D35: Subnormal subgroups 20E34: General structure theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 2 , October 1991 , pp. 331 - 342
Copyright
Copyright © Australian Mathematical Society 1991

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