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Finite Orders of Products of Two Class Transpositions Divide 840
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.
Related
- Groups of Class Transpositions with Prescribed Prime Divisors of the Moduli
- Ray class monoids for orders of number fields
- Element Orders and Character Codegrees of Finite Groups
- Finite groups with large sum of element orders compared to cyclic groups
- Schatten class membership of products of composition operators and their adjoints
BibTeX
@misc{iskra2026finite,
title = {{Finite Orders of Products of Two Class Transpositions Divide 840}},
author = {Alex Iskra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01793},
eprint = {2610.01793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01793},
}
RIS
TY - UNPB
TI - Finite Orders of Products of Two Class Transpositions Divide 840
AU - Alex Iskra
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01793
UR - https://arxiv.org/abs/2610.01793
AB - 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.
ER -