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A property of finitely generated residually finite groups
Published online by Cambridge University Press: 17 April 2009
Abstract
Let F(G) denote the set of isomorphism classes of finite quotients of the group G. We say that groups G and H have isomorphic finite quotients (IFQ) if F(G) = F(H). In this note, we show that a finitely generated residually finite group G cannot have the same finite quotients as a proper homomorphic image (G is IFQ hopfian). We then obtain some results on groups with the same finite quotients as a relatively free group.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 15 , Issue 3 , December 1976 , pp. 347 - 350
- Copyright
- Copyright © Australian Mathematical Society 1976
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