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: | , , |
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| Format: | Article |
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Cambridge University Press
2011
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/29669/ http://dx.doi.org/10.1017/S001708951100019X |
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| Summary: | 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. |
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