Author:
Grunewald Fritz,Segal Daniel
Abstract
Following P. F. Pickel (5) we write (G) for the set of isomorphism classes of finite quotients of a group G. One of the outstanding problems in the theory of polycyclic groups is to determine whether there can be infinitely many non-isomorphic polycyclic groups G with a given (G). We solve a special case of this problem with our first main result:Theorem 1. Let G be an abelian-by-cyclic polycyclic group. Then the polycyclic-by-finite groups H withlie in only finitely many isomorphism classes.
Publisher
Cambridge University Press (CUP)
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1. The genus of HNN-extensions;Mathematische Nachrichten;2012-12-27
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