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

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...

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Main Author: Alias, Idham Arif
Format: Article
Language:English
Published: Penerbit Universiti Kebangsaan Malaysia 2010
Online Access:http://psasir.upm.edu.my/id/eprint/12685/1/A%20description%20of%20an%20automorphism%20of%20a%20split%20metacyclic%20p.pdf
http://psasir.upm.edu.my/id/eprint/12685/
http://www.ukm.my/jsm/english_journals/vol39num6_2010/contentsVol39num6_2010.html
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spelling my.upm.eprints.126852018-10-16T07:51:34Z http://psasir.upm.edu.my/id/eprint/12685/ A description of an automorphism of a split metacyclic p-group Alias, Idham Arif 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. Penerbit Universiti Kebangsaan Malaysia 2010 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/12685/1/A%20description%20of%20an%20automorphism%20of%20a%20split%20metacyclic%20p.pdf Alias, Idham Arif (2010) A description of an automorphism of a split metacyclic p-group. Sains Malaysiana, 39 (6). pp. 1031-1034. ISSN 0026-6039 http://www.ukm.my/jsm/english_journals/vol39num6_2010/contentsVol39num6_2010.html
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description 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.
format Article
author Alias, Idham Arif
spellingShingle Alias, Idham Arif
A description of an automorphism of a split metacyclic p-group
author_facet Alias, Idham Arif
author_sort Alias, Idham Arif
title A description of an automorphism of a split metacyclic p-group
title_short A description of an automorphism of a split metacyclic p-group
title_full A description of an automorphism of a split metacyclic p-group
title_fullStr A description of an automorphism of a split metacyclic p-group
title_full_unstemmed A description of an automorphism of a split metacyclic p-group
title_sort description of an automorphism of a split metacyclic p-group
publisher Penerbit Universiti Kebangsaan Malaysia
publishDate 2010
url http://psasir.upm.edu.my/id/eprint/12685/1/A%20description%20of%20an%20automorphism%20of%20a%20split%20metacyclic%20p.pdf
http://psasir.upm.edu.my/id/eprint/12685/
http://www.ukm.my/jsm/english_journals/vol39num6_2010/contentsVol39num6_2010.html
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score 13.211869