发表机构
Sobolev Institute of Mathematics; Novosibirsk State University（索博列夫数学研究所; 新西伯利亚国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明两个类换位乘积的有限阶必整除840，回答Kourovka笔记本问题18.48，给出无限阶判定准则，并构造阶为840的实例证明界限紧。
AI 中文摘要
我们证明，如果两个类换位的乘积具有有限阶，则其阶整除840。这给出了Kourovka笔记本中问题18.48的完整肯定回答。我们还得到了两个类换位的乘积具有无限阶的判定准则。此外，我们构造了一对类换位，其乘积的阶为840，表明该界限是紧的。
英文摘要
We prove that if the product of two class transpositions has finite order, then its order divides 840. This gives a complete affirmative answer to Question 18.48 in the Kourovka Notebook. We also obtain a criterion for the product of two class transpositions to have infinite order. In addition, we construct a pair of class transpositions whose product has order 840, showing that the bound is sharp.
