Transforming Trees into Abelian Groups
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.