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Orders of Products of Horizontal Class Transpositions Full article

Journal Mathematical Notes
ISSN: 0001-4346 , E-ISSN: 1573-8876
Output data Year: 2025, Volume: 118, Number: 5-6, Pages: 921-932 Pages count : 12 DOI: 10.1134/s0001434625605520
Tags order of an element, involution, permutation, class transposition, graph
Authors Bardakov V.G. 1,2,3,4 , Iskra A.L. 1,4,5
Affiliations
1 Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090 Russia
2 Novosibirsk State Agrarian University, Novosibirsk, 630039 Russia
3 Regional Scientific and Educational Mathematical Center of Tomsk State University, Tomsk, 634050 Russia
4 Saint Petersburg State University, St. Petersburg, 199034 Russia
5 Novosibirsk State University, Novosibirsk, 630090 Russia

Funding (1)

1 Министерство науки и высшего образования РФ 075-15-2022-287

Abstract: 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 KourovkaNotebook. Weintroducethe setofhorizontal 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 numberin this set is the order of the product of some pair of horizontal class transpositions.
Cite: Bardakov V.G. , Iskra A.L.
Orders of Products of Horizontal Class Transpositions
Mathematical Notes. 2025. V.118. N5-6. P.921-932. DOI: 10.1134/s0001434625605520 WOS Scopus РИНЦ OpenAlex
Original: Бардаков В.Г. , Искра А.Л.
Порядки произведений горизонтальных транспозиций классов
Математические заметки. 2025. Т.118. №5. С.654-669. DOI: 10.4213/mzm14458 РИНЦ OpenAlex
Dates:
Submitted: Aug 2, 2024
Accepted: May 25, 2025
Published print: Apr 1, 2026
Published online: Apr 1, 2026
Identifiers:
≡ Web of science: WOS:001732652100039
≡ Scopus: 2-s2.0-105034801463
≡ Elibrary: 89161045
≡ OpenAlex: W7147738941
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