Nilpotent-by-finite groups with isomorphic finite quotients

Pickel, P. F.

doi:10.1090/S0002-9947-1973-0384940-6

Nilpotent-by-finite groups with isomorphic finite quotients
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Trans. Amer. Math. Soc. 183 (1973), 313-325 Request permission

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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