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Small Groups of Automorphisms

Small Groups of Automorphisms 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Oxford University Press

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References (11)

Publisher
Oxford University Press
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/S0024609397004037
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Bulletin of the London Mathematical SocietyOxford University Press

Published: Jul 1, 1998

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