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SMALL GROUPS OF AUTOMORPHISMS

Published online by Cambridge University Press:  01 July 1998

P. P. PÁLFY  and
L. PYBER
P. P. PÁLFY
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, Budapest, P.O. Box 127, H-1364 Hungary
L. PYBER
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, Budapest, P.O. Box 127, H-1364 Hungary
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Abstract

Let A be a group of automorphisms of the finite group G such that ([mid ]A[mid ], [mid ]G[mid ])=1. Then [mid ]A[mid ]<[mid ]G[mid ]2, and the exponent 2 here is best possible. If, moreover, A is nilpotent of class at most 2, then [mid ]A[mid ]<[mid ]G[mid ]. If A is abelian, then A has a regular orbit on G.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 4 , July 1998 , pp. 386 - 390
Copyright
© The London Mathematical Society 1998

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