Abstract

We introduce a new class of torsion-free abelian groups which are special epimorphic images of finite rank completely decomposable groups. They belong to the well-known class of Butler groups by their definition. In comparison with the existing results the presented groups are not only of the maximal possible rank that is obviously less than the rank of the pre-image. The kernel of the above epimorphism admits a special matrix representation. The number of matrix rows is equal to the kernel rank and the number of its columns coincides with the preimage rank. By finitely many suitable operations the original matrix representation can be deduced to a special trapezoid form which corresponds to another choice of the epimorphism kernel generators. This matrix form clarifies the properties of the image that is exactly a group under investigation.

For this class of torsion-free abelian groups of finite rank a strong indecomposability criterion is proved on the basis of their matrix representation.

中文翻译：

---

不可分解的管家群

摘要

我们引入了一类新的无扭阿贝尔群，它们是有限秩完全可分解群的特殊表观像。根据他们的定义，他们属于著名的巴特勒群体。与现有结果相比，所呈现的组不仅是最大可能的秩，显然小于原像的秩。上述表同态的核允许一种特殊的矩阵表示。矩阵行数等于核秩，列数与原像秩一致。通过有限多个合适的运算，原始矩阵表示可以推导出特殊的梯形形式，该形式对应于另一种外同态核生成器的选择。这种矩阵形式阐明了图像的属性，该图像正是被调查的组。

对于这类有限秩的无扭阿贝尔群，基于它们的矩阵表示证明了强不可分解准则。