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Transactions of the American Mathematical Society

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

 

 

Nilpotent-by-finite groups with isomorphic finite quotients


Author: P. F. Pickel
Journal: Trans. Amer. Math. Soc. 183 (1973), 313-325
MSC: Primary 20E99
DOI: https://doi.org/10.1090/S0002-9947-1973-0384940-6
MathSciNet review: 0384940
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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)$. Let $ \mathcal{H}$ denote the class of finite extensions of finitely generated nilpotent groups. In this paper we show that if G is in $ \mathcal{H}$, then the groups H in $ \mathcal{H}$ for which $ \mathcal{F}(G) = \mathcal{F}(H)$ lie in only finitely many isomorphism classes.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0384940-6
Article copyright: © Copyright 1973 American Mathematical Society