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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Finitely generated nilpotent groups with isomorphic finite quotients

Author: P. F. Pickel
Journal: Trans. Amer. Math. Soc. 160 (1971), 327-341
MSC: Primary 20F05
MathSciNet review: 0291287
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Abstract: Let $ \mathcal{F}(G)$ denote the set of isomorphism classes of finite homomorphic images of a group $ G$. We say that groups $ G$ and $ H$ have isomorphic finite quotients if $ \mathcal{F}(G) = \mathcal{F}(H)$. In this paper we show that if $ G$ is a finitely generated nilpotent group, the finitely generated nilpotent groups $ H$ for which $ \mathcal{F}(G) = \mathcal{F}(H)$) lie in only finitely many isomorphism classes. This is done using some finiteness results from the theory of algebraic groups along with some heretofore unpublished results of A. Borel.

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Keywords: Isomorphic finite quotients, arithmetic groups, algebraic groups, Lie algebras
Article copyright: © Copyright 1971 American Mathematical Society

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