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ON THE ORDERS OF AUTOMORPHISM GROUPS OF FINITE GROUPS

Published online by Cambridge University Press:  01 June 2005

JOHN N. BRAY  and
ROBERT A. WILSON
JOHN N. BRAY
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United KingdomJ.N.Bray@qmul.ac.uk, R.A.Wilson@qmul.ac.uk
ROBERT A. WILSON
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United KingdomJ.N.Bray@qmul.ac.uk, R.A.Wilson@qmul.ac.uk
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Abstract

In the Kourovka notebook, Deaconescu asks whether $\gpord{\Aut G}\ge \phi(\gpord{G})$ for all finite groups $G$, where $\phi$ denotes the Euler totient function, and whether $G$ is cyclic whenever $\gpord{\Aut G}= \phi(\gpord{G})$. Both questions are answered in the negative in this paper. Moreover, $\gpord{\Aut G}/ \phi(\gpord{G)$ can be made arbitrarily small.

Keywords

20E36 (primary)20F28 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 3 , June 2005 , pp. 381 - 385
Copyright
© The London Mathematical Society 2005

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Footnotes

This research was carried out while both authors were at the University of Birmingham.