Splitting length of Abelian mixed groups of torsion-free rank 1

Pham Thi Thu Thuy

M. V. Lomonosov Moscow State University

Abstract: Splitting length of a mixed Abelian group $G$ is defined as the smallest positive integer $n$ such that $\bigotimes\limits^nG$ splits. The task of determining the splitting length of mixed Abelian groups was formulated by Irwin, Khabbaz, and Rayna. In this paper, a criterion for determining whether $\bigotimes\limits^nG$ splits for countable mixed Abelian groups $G$ of torsion-free rank 1 is found.

UDC: 512.541

 English version: Journal of Mathematical Sciences (New York), 2010, 164:2, 294–302

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