Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-23T05:28:27.459Z Has data issue: false hasContentIssue false
  • English
  • Français

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 [email protected], [email protected]
ROBERT A. WILSON
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United [email protected], [email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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