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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2011
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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 |
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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 |
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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 |
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13.160551 |