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A description of an automorphism of a non-split metacyclic p-group

Alias, Idham Arif (2011) A description of an automorphism of a non-split metacyclic p-group. Pertanika Journal of Science & Technology, 19 (1). pp. 109-116. ISSN 0128-7680; ESSN: 2231-8526

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A map on a group is not necessarily an automorphism on the group. In this paper we study the necessary and sufficient conditions for a map on a non-split metacyclic p-group to be an automorphism, where we only consider p as an odd prime number. The metacyclic group can be defined by a presentation and it will be beneficial to have a direct relation between the parameters in the presentation and an automorphism of the group. We consider the action of an automorphism on the generators of the group mentioned. Since any element of a metacyclic group will be mapped to an element of the group by an automorphism, we can conveniently represent the automorphism in a matrix notation. We then use the relations and the regularity of the non-split metacyclic p-group to find conditions on each entry of the matrix in terms of the parameters in its presentation so that such a matrix does indeed represent an automorphism.

Item Type:Article
Keyword:Automorphism; Matrix notation; Non-split metacyclic p-group
Faculty or Institute:Faculty of Science
Institute for Mathematical Research
Publisher:Universiti Putra Malaysia Press
ID Code:12684
Deposited By: Nurul Ainie Mokhtar
Deposited On:22 Jun 2015 08:41
Last Modified:22 Jun 2015 08:41

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