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

Idham Arif Alias, (2010) A description of an automorphism of a split metacyclic p-group. Sains Malaysiana, 39 (6). pp. 1031-1034. ISSN 0126-6039


Official URL: http://www.ukm.my/jsm/english_journals/vol39num6_2...


A map on a group is not necessarily an automorphism on the group. In this paper we determined the necessary and sufficient conditions of a map on a split metacyclic p-group to be an automorphism, where we only considered 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 considered 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 used the relations and the regularity of the 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
Keywords:Automorphism; matrix representation; split metacyclic p-group
Journal:Sains Malaysiana
ID Code:7449
Deposited By: Mr Fazli Nafiah -
Deposited On:13 Aug 2014 08:17
Last Modified:14 Dec 2016 06:44

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