Automorphism groups of metacyclic groups of class two

An automorphism of a group G is an isomorphism from G to G, which is one to one, onto and preserving operation. The automorphism of G forms a group under composition, and is denoted as Aut ?G?. A group is metacyclic if there is a normal cyclic subgroup whose quotient group is also cyclic. In 1973, K...

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Main Author:	A. Mohamed, Abir Naser
Format:	Thesis
Language:	English
Published:	2011
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/47952/25/AbirNaserAMohamedMFS2011.pdf
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id	my-utm-ep.47952
record_format	uketd_dc
spelling	my-utm-ep.479522018-05-30T03:39:26Z Automorphism groups of metacyclic groups of class two 2011-07 A. Mohamed, Abir Naser QA Mathematics An automorphism of a group G is an isomorphism from G to G, which is one to one, onto and preserving operation. The automorphism of G forms a group under composition, and is denoted as Aut ?G?. A group is metacyclic if there is a normal cyclic subgroup whose quotient group is also cyclic. In 1973, King classified metacyclic p ? group while in 1987, Newman developed a new approach to metacyclic p ? groups suggested by the p ? group generation algorithm. They found new presentation for these groups. The automorphism groups can be separated to inner and outer automorphisms. An inner automorphism is an automorphism corresponding to conjugation by some element a. The set of all automorphisms form a normal subgroup of Aut ?G?. The automorphism group which is not inner is called outer automorphism and denoted as Out ?G?. In this research, automorphism groups of split and non-split metacyclic groups of class two will be investigated including the inner and outer automorphisms. 2011-07 Thesis http://eprints.utm.my/id/eprint/47952/ http://eprints.utm.my/id/eprint/47952/25/AbirNaserAMohamedMFS2011.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics A. Mohamed, Abir Naser Automorphism groups of metacyclic groups of class two
description	An automorphism of a group G is an isomorphism from G to G, which is one to one, onto and preserving operation. The automorphism of G forms a group under composition, and is denoted as Aut ?G?. A group is metacyclic if there is a normal cyclic subgroup whose quotient group is also cyclic. In 1973, King classified metacyclic p ? group while in 1987, Newman developed a new approach to metacyclic p ? groups suggested by the p ? group generation algorithm. They found new presentation for these groups. The automorphism groups can be separated to inner and outer automorphisms. An inner automorphism is an automorphism corresponding to conjugation by some element a. The set of all automorphisms form a normal subgroup of Aut ?G?. The automorphism group which is not inner is called outer automorphism and denoted as Out ?G?. In this research, automorphism groups of split and non-split metacyclic groups of class two will be investigated including the inner and outer automorphisms.
format	Thesis
qualification_level	Master's degree
author	A. Mohamed, Abir Naser
author_facet	A. Mohamed, Abir Naser
author_sort	A. Mohamed, Abir Naser
title	Automorphism groups of metacyclic groups of class two
title_short	Automorphism groups of metacyclic groups of class two
title_full	Automorphism groups of metacyclic groups of class two
title_fullStr	Automorphism groups of metacyclic groups of class two
title_full_unstemmed	Automorphism groups of metacyclic groups of class two
title_sort	automorphism groups of metacyclic groups of class two
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2011
url	http://eprints.utm.my/id/eprint/47952/25/AbirNaserAMohamedMFS2011.pdf
_version_	1747817271617650688

Automorphism groups of metacyclic groups of class two

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