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Strong genus of nilpotent groups of Hirsch length six

Published online by Cambridge University Press:  01 September 1999

CHARLES CASSIDY
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec G1K 7P4, Canada. e-mail: [email protected]
DIRK SCEVENELS
Affiliation:
Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B–3001 Heverlee, Belgium. e-mail: [email protected]

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 MpNp for every prime p, then MPNP for every finite set of primes P).

Type
Research Article
Copyright
The Cambridge Philosophical Society 1999

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