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ON THE CAPABILITY OF FINITELY GENERATED NON-TORSION GROUPS OF NILPOTENCY CLASS 2

Published online by Cambridge University Press:  21 March 2011

LUISE-CHARLOTTE KAPPE ,
NOR MUHAINIAH MOHD ALI  and
NOR HANIZA SARMIN
LUISE-CHARLOTTE KAPPE
Affiliation:
Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USA e-mail: menger@math.binghamton.edu
NOR MUHAINIAH MOHD ALI
Affiliation:
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia e-mail: normuhainiah@utm.my, nhs@utm.my
NOR HANIZA SARMIN
Affiliation:
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia e-mail: normuhainiah@utm.my, nhs@utm.my
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Abstract

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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.

Keywords

20D1520J05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 2 , May 2011 , pp. 411 - 417
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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