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On a Theorem of Goldschmidt Applied to Groups with a Coprime Automorphism

Published online by Cambridge University Press:  20 November 2018

Martin R. Pettet
Martin R. Pettet*
Affiliation:
University of Wisconsin, Madison, Wisconsin
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In a recent important paper of Goldschmidt [3], all finite simple groups were determined in which a non-trivial abelian 2-subgroup controls 2-fusion. Our purpose here is to present a straightforward application of this deep result to the following general question: If p is a prime and G is a finite group of order not divisible by p which admits an automorphism σ of order pn, what conditions on the fixed point subgroup CG(σ) will ensure that G is solvable?

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 201 - 206
Copyright
Copyright © Canadian Mathematical Society 1976

References

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