A NOTE ON NIELSEN EQUIVALENCE IN FINITELY GENERATED ABELIAN GROUPS

Authors

  • Daniel Oancea

Keywords:

Nielsen transformations, abelian groups

Abstract

Nielsen transformations determine the automorphisms of a free group of rank n, and also of a free abelian group of rank n, and furthermore the generating n-tuples of such groups form a single Nielsen equivalence class. For an arbitrary rank n group, the generating n-tuples may fall into several Nielsen classes. Diaconis and Graham determined the Nielsen classes for finite abelian groups. We extend their result to the case of infinite abelian groups.

Published

2011-10-19

Issue

Vol. 84 No. 1 (2011)

Section

Articles
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