On the capability of finitely generated non-torsion groups of nilpotency class 2

A group is called capable if it is a central factor group. In this paper, we establish a necessary condition for a finitely generated non-torsion group of nilpotency class 2 to be capable. Using the classification of two-generator non-torsion groups of nilpotency class 2, we determine which of them...

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Main Authors:	Kappe, Luise-Charlotte, Mohd. Ali, Nor Muhainiah, Sarmin, Nor Haniza
Format:	Article
Published:	Cambridge University Press 2011
Subjects:	Q Science
Online Access:	http://eprints.utm.my/id/eprint/29669/ http://dx.doi.org/10.1017/S001708951100019X
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Institution:	Universiti Teknologi Malaysia

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spelling	my.utm.296692017-10-17T04:48:11Z http://eprints.utm.my/id/eprint/29669/ On the capability of finitely generated non-torsion groups of nilpotency class 2 Kappe, Luise-Charlotte Mohd. Ali, Nor Muhainiah Sarmin, Nor Haniza Q Science A group is called capable if it is a central factor group. In this paper, we establish a necessary condition for a finitely generated non-torsion group of nilpotency class 2 to be capable. Using the classification of two-generator non-torsion groups of nilpotency class 2, we determine which of them are capable and which are not and give a necessary and sufficient condition for a two-generator non-torsion group of class 2 to be capable in terms of the torsion-free rank of its factor commutator group. Cambridge University Press 2011 Article PeerReviewed Kappe, Luise-Charlotte and Mohd. Ali, Nor Muhainiah and Sarmin, Nor Haniza (2011) On the capability of finitely generated non-torsion groups of nilpotency class 2. Glasgow Mathematical Journal, 53 (2). pp. 411-417. ISSN 1469-509X http://dx.doi.org/10.1017/S001708951100019X 10.1017/S001708951100019X
institution	Universiti Teknologi Malaysia
building	UTM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Teknologi Malaysia
content_source	UTM Institutional Repository
url_provider	http://eprints.utm.my/
topic	Q Science
spellingShingle	Q Science Kappe, Luise-Charlotte Mohd. Ali, Nor Muhainiah Sarmin, Nor Haniza On the capability of finitely generated non-torsion groups of nilpotency class 2
description	A group is called capable if it is a central factor group. In this paper, we establish a necessary condition for a finitely generated non-torsion group of nilpotency class 2 to be capable. Using the classification of two-generator non-torsion groups of nilpotency class 2, we determine which of them are capable and which are not and give a necessary and sufficient condition for a two-generator non-torsion group of class 2 to be capable in terms of the torsion-free rank of its factor commutator group.
format	Article
author	Kappe, Luise-Charlotte Mohd. Ali, Nor Muhainiah Sarmin, Nor Haniza
author_facet	Kappe, Luise-Charlotte Mohd. Ali, Nor Muhainiah Sarmin, Nor Haniza
author_sort	Kappe, Luise-Charlotte
title	On the capability of finitely generated non-torsion groups of nilpotency class 2
title_short	On the capability of finitely generated non-torsion groups of nilpotency class 2
title_full	On the capability of finitely generated non-torsion groups of nilpotency class 2
title_fullStr	On the capability of finitely generated non-torsion groups of nilpotency class 2
title_full_unstemmed	On the capability of finitely generated non-torsion groups of nilpotency class 2
title_sort	on the capability of finitely generated non-torsion groups of nilpotency class 2
publisher	Cambridge University Press
publishDate	2011
url	http://eprints.utm.my/id/eprint/29669/ http://dx.doi.org/10.1017/S001708951100019X
_version_	1643648350586667008

On the capability of finitely generated non-torsion groups of nilpotency class 2

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