TY - JOUR

T1 - Orders of Products of Horizontal Class Transpositions

AU - Бардаков, Валерий Георгиевич

AU - Искра, Алекс Львович

N1 - Bardakov, V.G., Iskra, A.L. Orders of Products of Horizontal Class Transpositions. Math Notes 118, 921–932 (2025). This work was carried out at St. Petersburg Euler International Mathematical Institute under the financial support of the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-287 of April 6, 2022).

PY - 2025/12

Y1 - 2025/12

N2 - The group CT(Z) of class transpositions was introduced by S. Kohl in 2010. This is a countable subgroup of the group Sym(Z) of all permutations on the set Z of integers. We study products of two class transpositions in CT(Z) and give a partial answer to Kohl’s Question 18.48 in The Kourovka Notebook. We introduce the set of horizontal class transpositions and prove that the order of the product of two horizontal class transpositions belongs to the set {1, 2, 3, 4, 6, 12} and any number in this set is the order of the product of some pair of horizontal class transpositions.

AB - The group CT(Z) of class transpositions was introduced by S. Kohl in 2010. This is a countable subgroup of the group Sym(Z) of all permutations on the set Z of integers. We study products of two class transpositions in CT(Z) and give a partial answer to Kohl’s Question 18.48 in The Kourovka Notebook. We introduce the set of horizontal class transpositions and prove that the order of the product of two horizontal class transpositions belongs to the set {1, 2, 3, 4, 6, 12} and any number in this set is the order of the product of some pair of horizontal class transpositions.

KW - order of an element

KW - involution

KW - permutation

KW - class transposition

KW - graph

UR - https://www.scopus.com/pages/publications/105034801463

U2 - 10.1134/S0001434625605520

DO - 10.1134/S0001434625605520

M3 - Article

VL - 118

SP - 921

EP - 932

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 5-6

ER -