Transforming Trees into Abelian Groups


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New Zealand Journal of Mathematics

Vol. 41, (2011), Pages 75-81

Alexander G. Melnikov

Department of Computer Science

The University of Auckland

Auckland, New Zealand

Abstract We study a coding of trees into torsion-free abelian groups which proved to be useful in effective algebra. We show that this transformation is not injective. Furthermore, we show that for the class of finite trees having all leaves at the same level, the resulting groups are isomorphic if and only if the underlying trees have the same number of nodes at corresponding levels.

Keywords abelian groups, effective transformations

Classification (MSC2000) 20K99.

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