TY - JOUR

T1 - Orders of products of slanted class transpositions

AU - Bardakov, Valery G.

AU - Iskra, Alex L.

N1 - The work was supported by the Russian Science Foundation, project 24-11-00119, https://rscf.ru/en/project/24-11-00119/.

PY - 2026/1/17

Y1 - 2026/1/17

N2 - We study the orders of products of two class transpositions in the group CT(Z), a simple subgroup of the symmetric group on the integers. For pairs of class transpositions sharing a common vertex, we prove that the order of their product is either 1, 3, or ∞, and provide a precise criterion for the infinite order case. Furthermore, we investigate pairs of equal-residue and equal-modulus class transpositions, establishing conditions under which their product has finite or infinite order. Our results provide a partial answer to a question posed in the Kourovka notebook (see Question 18.48).

AB - We study the orders of products of two class transpositions in the group CT(Z), a simple subgroup of the symmetric group on the integers. For pairs of class transpositions sharing a common vertex, we prove that the order of their product is either 1, 3, or ∞, and provide a precise criterion for the infinite order case. Furthermore, we investigate pairs of equal-residue and equal-modulus class transpositions, establishing conditions under which their product has finite or infinite order. Our results provide a partial answer to a question posed in the Kourovka notebook (see Question 18.48).

UR - https://www.scopus.com/pages/publications/105027998435

UR - https://www.mendeley.com/catalogue/0b594062-b88c-3dc3-8bba-bcb5ebf27ec2/

U2 - 10.1515/jgth-2025-0074

DO - 10.1515/jgth-2025-0074

M3 - Article

JO - Journal of Group Theory

JF - Journal of Group Theory

SN - 1433-5883

ER -