J Austral Math Soc Ser A 51 pp331--342, 1991.

Groups of Odd Order in which Every Subnormal Subgroup has Defect at Most Two

John Cossey

Abstract

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 the 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 of defect at most two has derived and Fitting length at most three, and these bounds are best possible.

1980 AMS Subject Classification (1985 Revision): 20D35, 20E34

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Authors

John Cossey

Department of Mathematics, A.N.U., GPO Box 4, Canberra, ACT 2601, Australia.