Direct products and the Hopf property

Author:

Jones J. M. Tyrer

Abstract

In [1] Neumann and Dey prove that the free product of two finitely generated Hopf groups is Hopf and ask whether a similar result holds for direct products. It is the purpose of this paper to show that this is not the case. We proveTHEOREM A. There exists a finitely generated group G satisfying the following conditions:(i) G is isomorphic to a proper direct factor of itself;(ii) G is the direct product of two Hopf groups.

Publisher

Cambridge University Press (CUP)

Reference5 articles.

1. Simple Free Products

2. The Hopf property of free products

3. [3] Tyrer J. M. , ‘On Direct Products and the Hopf Property’, D. Phil. Thesis, University of Oxford, (1971).

4. An essay on free products of groups with amalgamations

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