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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
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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?
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- Copyright © Canadian Mathematical Society 1976
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