Abstract

It is proved that for two different classes of torsion-free abelian groups the direct decomposability properties coincide with respect to the quotients of indecomposable summands over their regulators. The method used is embedding almost rigid groups as fully invariant subgroups in some Butler groups of infinite rank with determination of their decomposition theory.

中文翻译：

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无扭转阿贝尔群的直接分解

摘要

事实证明，对于两类不同的无扭转阿贝尔群，其直接可分解性与调节器上不可分解乘数的商一致。确定其分解理论的方法是将几乎刚性的组作为完全不变的子组嵌入到一些无限级的Butler组中。