Orders of products of slanted class transpositions

Orders of products of slanted class transpositions Full article

Journal

Journal of Group Theory
ISSN: 1433-5883

Output data

Year: 2026, DOI: 10.1515/jgth-2025-0074

Authors

Bardakov Valery G. ^1,2,3 , Iskra Alex L. ^1,4

Affiliations

1	Sobolev Institute of Mathematics , 4 Acad. Koptyug avenue, 630090 , Novosibirsk;
2	Novosibirsk State Agrarian University, Dobrolyubova street, 160, Novosibirsk, 630039;
3	Regional Scientific and Educational Mathematical Center of Tomsk State University, 36 Lenin Ave., Tomsk , Russia
4	Novosibirsk State University, 2 Pirogova Street, 630090 , Novosibirsk , Russia

Funding (1)

Russian Science Foundation

24-11-00119

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 \infty, 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).

Bardakov V.G. , Iskra A.L.
Orders of products of slanted class transpositions
Journal of Group Theory. 2026. DOI: 10.1515/jgth-2025-0074

Submitted:

May 9, 2025

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