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On Finite Soluble Groups

Published online by Cambridge University Press:  09 April 2009

J. N. Ward
J. N. Ward
Affiliation:
Mathematics Institute University of Warwick
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Let p be a class of finite soluble groups which is closed under epimorphic images and let g be a saturated formation. Then if G is a group of minimal order belonging to p but not to g, F(G), the Fitting subgroup of G, is the unique minimal normal subgroup of G. It is to groups with this property that the following proposition is applicable.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 1-2 , February 1969 , pp. 250 - 251
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Ward, J. N., ‘Involutory Automorphisms of Groups of Odd Order’, J. Australian Math. Soc. 6 (1966), 480–494.CrossRefGoogle Scholar
[2]Wielandt, H., ‘Über Produkte von Nilpotenten Gruppen’, Illinois J. Math. 2 (1959), 611–618.Google Scholar