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On polycyclic groups with isomorphic finite quotients

Published online by Cambridge University Press:  24 October 2008

Fritz Grunewald  and
Daniel Segal
Fritz Grunewald
Affiliation:
Universität Bielefeld, W. Germany
Daniel Segal
Affiliation:
Universität Bielefeld, W. Germany
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 2 , September 1978 , pp. 235 - 246
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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