This paper examines the constricted use of group theory in the studies of pairwise comparisons. The presented approach is based on the application of the famous Levi Theorems of 1942 and 1943 for orderable groups. The theoretical foundation for multiplicative (ratio) pairwise comparisons has been provided. Counterexamples have been provided to support the theory. In our opinion, the scientific community must be made aware of the limitations of using the group theory in pairwise comparisons. Groups, which are not torsion free, cannot be used for ratios by Levi's theorems.

中文翻译：

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关于使用群论来概括成对比较矩阵的元素：注意事项

本文考察了在成对比较研究中对群论的限制使用。所提出的方法基于 1942 年和 1943 年著名的列维定理对可排序群的应用。提供了乘法（比率）成对比较的理论基础。已经提供了反例来支持该理论。我们认为，科学界必须意识到在成对比较中使用群论的局限性。非无扭转群不能用于李维斯定理的比率。