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Solubility theorems for finite groups

Published online by Cambridge University Press:  24 October 2008

Thomas J. Laffey
Thomas J. Laffey
Affiliation:
University College, Dublin
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Extract

In this paper we obtain various sufficient conditions for the solubility of a finite group. In particular, we show that if G is a finite group and p≥5 is a prime such that all p′-subgroups of G are nilpotent, then G is soluble. We show also that if G is a finite group which has a cyclic Sylow p-subgroup Pand such that for all p′-subgroups H of G, H is nilpotent and H′ is cyclic, then, if p≠3, either P◃G or G has a normal p-complement.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 1 - 6
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

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