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Elementary equivalence and genus of finitely generated nilpotent groups

Published online by Cambridge University Press:  17 April 2009

Francis Oger
Francis Oger
Affiliation:
Département de Mathématiques, Université Paris VII2 place Jussieu, 75.251 Paris Cedex 05, France 12 rue de la Gare, 89.410 Cézy, France.
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Abstract

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We show that, if two finitely generated nilpotent groups are elementarily equivalent, and more generally if they satisfy the same sentences with one alternation of quantifiers, then, they are quite similar, though not necessarily isomorphic. For instance, each of them is isomorphic to a subgroup of finite index of the other and they have the same finite images, the same Mislin genus and the same Pickel genus.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 1 , February 1988 , pp. 61 - 68
Copyright
Copyright © Australian Mathematical Society 1988

References

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