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ON THE CENTRE OF THE AUTOMORPHISM GROUP OF A GROUP
Published online by Cambridge University Press: 16 June 2015
Abstract
If the centre of a group $G$ is trivial, then so is the centre of its automorphism group. We study the structure of the centre of the automorphism group of a group $G$ when the centre of $G$ is a cyclic group. In particular, it is shown that the exponent of $Z(\text{Aut}(G))$ is less than or equal to the exponent of $Z(G)$ in this case.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 92 , Issue 3 , December 2015 , pp. 390 - 396
- Copyright
- © 2015 Australian Mathematical Publishing Association Inc.