Finite Orders of Products of Two Class Transpositions Divide 840

Source 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.