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Finite groups admitting fixed point free automorphisms of order pq

Published online by Cambridge University Press:  20 January 2009

Cheng Kai-Nah
Cheng Kai-Nah
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 0511
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By the results of Rickman [7] and Ralston [6], a finite group G admitting a fixed point free automorphism α of order pq, where p and q are primes, is soluble. If p = q, then |G| is necessarily coprime to |α|, and it follows from Berger [1] that G has Fitting height at most 2, the composition length of <α>. The purpose of this paper is to prove a corresponding result in the case when p≠q.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 1 , February 1987 , pp. 51 - 56
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

REFERENCES

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