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arXiv · 2610.01793

Finite Orders of Products of Two Class Transpositions Divide 840

Alex Iskra
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Abstract

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.

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Alex Iskra. 2026-10-01. Finite Orders of Products of Two Class Transpositions Divide 840. https://arxiv.org/abs/2610.01793

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