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Metabelian groups with the same finite quotients

Published online by Cambridge University Press:  17 April 2009

P.F. Pickel
P.F. Pickel
Affiliation:
Department of Mathematics, Polytechnic Institute of New York, Brooklyn, New York, USA.
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Abstract

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Let F(G) denote the set of isomorphism classes of finite quotients of the group G. Two groups G and H are said to have the same finite quotients if F(G) = F(H). We construct infinitely many nonisomorphic finitely presented metabelian groups with the same finite quotients, using modules over a suitably chosen ring. These groups also give an example of infinitely many nonisomorphic split extensions of a fixed finitely presented metabelian group by a fixed finite abelian group, all having the same finite quotients.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 1 , August 1974 , pp. 115 - 120
Copyright
Copyright © Australian Mathematical Society 1974

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