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On normal subgroups of direct products

Published online by Cambridge University Press:  20 January 2009

F. E. A. Johnson
F. E. A. Johnson
Affiliation:
University College London, Gower Street, London WC1E 6BT, UK
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Abstract

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We investigate the equivalence classes of normal subdirect products of a product of free groups Fn1 × … × Fnk under the simultaneous equivalence relations of commensurability and conjugacy under the full automorphism group. By abelianisation, the problem is reduced to one in the representation theory of quivers of free abelian groups. We show there are infinitely many such classes when k≧3, and list the finite number of classes when k = 2.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 2 , June 1990 , pp. 309 - 319
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

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