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Strong genus of nilpotent groups of Hirsch length six
Published online by Cambridge University Press: 01 September 1999
Abstract
We give a characterization in terms of finitely many arithmetical invariants for two finitely generated, torsion-free, nilpotent groups of nilpotency class two and Hirsch length six to have isomorphic localizations at every finite set of primes. This result is obtained through adequate reduction of an arbitrary binary integral quadratic form. We derive some consequences and, in particular, we characterize completely those groups N in the above class of groups, for which the Mislin genus coincides with the strong genus (i.e. those groups N for which, whenever a nilpotent group M satisfies Mp ≅ Np for every prime p, then MP ≅ NP for every finite set of primes P).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 2 , September 1999 , pp. 207 - 216
- Copyright
- The Cambridge Philosophical Society 1999