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Abstract Let A be a group of automorphisms of the finite group G such that (∣A∣, ∣G∣)=1. Then ∣A∣<∣G∣2, and the exponent 2 here is best possible. If, moreover, A is nilpotent of class at most 2, then ∣A∣<∣G∣. If A is abelian, then A has a regular orbit on G. 1991 Mathematics Subject Classification 20D45. © London Mathematical Society
Bulletin of the London Mathematical Society – Oxford University Press
Published: Jul 1, 1998
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