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Bulletin of the London Mathematical Society Advance Access originally published online on December 21, 2007
Bulletin of the London Mathematical Society 2007 39(6):973-981; doi:10.1112/blms/bdm102
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© 2007 London Mathematical Society

On the Fitting height of a soluble group that is generated by a conjugacy class of 3-elements

Abdullah Al-Roqi

Department of Mathematics
College of Science
King Abdulaziz University
P.O.Box 80203
Jeddah 21589
Saudi Arabia

Paul Flavell

School of Mathematics
The University of Birmingham
Birmingham B15 2TT
United Kingdom
P.J.Flavell@bham.ac.uk

Received 25 November 2006. Revision received 3 July 2007.

Let G be a finite soluble group that is generated by a conjugacy class consisting of elements of order 3. We show that there exist four conjugates of an element of order 3 that generate a subgroup with the same Fitting height as G. We use this result to find a soluble analogue of the Baer–Suzuki theorem in the case prime 3.

2000 Mathematics Subject Classification 20D10.

This work is a part of the first author's PhD thesis.


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