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Genus of nilpotent groups of Hirsch length six

Published online by Cambridge University Press:  24 October 2008

Charles Cassidy  and
Caroline Lajoie
Charles Cassidy
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec, Canada
Caroline Lajoie
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec, Canada
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Abstract

In this paper, we characterize the genus of an arbitrary torsion-free finitely generated nilpotent group of class two and of Hirsch length six by means of a finite number of arithmetical invariants. An algorithm which permits the enumeration of all possible genera that can occur under the conditions above is also given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 3 , May 1995 , pp. 431 - 438
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

REFERENCES

[1]Casacuberta, C., Cassidy, C. and From, Y. El. Extended genus of torsion-free finitely generated nilpotent groups of class two (Preprint 1993).Google Scholar
[2]Grunewald, F. J. and Scharlau, R.. A note on finitely generated torsion-free nilpotent groups of class 2. J. Algebra 58 (1979), 162–175.CrossRefGoogle Scholar
[3]Grunewald, F. J., Segal, D. and Sterling, L. S.. Nilpotent groups of Hirsch length six. Math. Z. 179 (1982), 219–235.CrossRefGoogle Scholar
[4]Mislin, G.. Nilpotent groups with finite commutator subgroups. Lecture Notes in Math. 418 (Springer-Verlag, 1974), 103–118.Google Scholar
[5]Oger, F.. Des groupes nilpotents de classe 2 sans torsion de type fini ayant les mêmes images finies peuvent ne pas être élémentairement équivalents. C. R. Acad. Sc. Paris, Ser. A 294 (4 janvier 1982).Google Scholar
[6]Pickel, P. F.. Finitely generated nilpotent groups with isomorphic finite quotients. Trans. Amer. Math. Soc. 160 (1971), 327–341.CrossRefGoogle Scholar
[7]Segal, D.. Polycyclic groups (Cambridge University Press, 1983).CrossRefGoogle Scholar
[8]Sterling, L. S.. Computing invariants for finitely generated nilpotent groups. Ph.D. thesis, Australian National University (1981).CrossRefGoogle Scholar
[9]Warfield, R. B.. Genus and cancellation for groups with finite commutator subgroup. J. Pure Appl. Alg. 6 (1975), 125–132.CrossRefGoogle Scholar