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More generalised Sylow theorems

Published online by Cambridge University Press:  09 April 2009

I. J. Hawthorn
Affiliation:
Department of Mathematics University of WaikatoPrivate Bag 3105 HamiltonNew Zealand e-mail: [email protected]
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Abstract

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The study of classes of finite groups is divided into two parts. The projective theory studies formations and Schunck classes. The dual injective theory studies Fitting classes. In each type of class a generalisation of Sylow's theorem holds. In this paper we seek further generalisations of Sylow's theorem which hold for classes which are neither injective nor projective, but obey other related properties. Firstly a common framework for the injective and projective theories is constructed. Within the context of this common framework further types of Sylow theorem can then be sought. An example is given of a property which is a simple hybrid of injectivity and projectivity which we will call ‘interjectivity’. A generalised Sylow theorem is then proved in the interjective case.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Doerk, Klaus and Hawkes, Trevor, ‘Finite soluble groups’, in: Expositions in mathematics A (De Gruyter, Berlin, 1992).Google Scholar