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The Group of Generalized Class Transpositions and its Automorphisms. / Neshchadim, M. V.; Neshchadim, S. M.

In: Siberian Advances in Mathematics, Vol. 35, No. 3, 09.2025, p. 221-228.

Research output: Contribution to journal › Article › peer-review

Harvard

Neshchadim, MV & Neshchadim, SM 2025, 'The Group of Generalized Class Transpositions and its Automorphisms', Siberian Advances in Mathematics, vol. 35, no. 3, pp. 221-228. https://doi.org/10.1134/S1055134425030058

APA

Neshchadim, M. V., & Neshchadim, S. M. (2025). The Group of Generalized Class Transpositions and its Automorphisms. Siberian Advances in Mathematics, 35(3), 221-228. https://doi.org/10.1134/S1055134425030058

Vancouver

Neshchadim MV, Neshchadim SM. The Group of Generalized Class Transpositions and its Automorphisms. Siberian Advances in Mathematics. 2025 Sept;35(3):221-228. doi: 10.1134/S1055134425030058

Author

Neshchadim, M. V. ; Neshchadim, S. M. / The Group of Generalized Class Transpositions and its Automorphisms. In: Siberian Advances in Mathematics. 2025 ; Vol. 35, No. 3. pp. 221-228.

BibTeX

@article{9d2868b55f84458fb0e849a1f8d7183a,
title = "The Group of Generalized Class Transpositions and its Automorphisms",
abstract = "We introduce a group ECT(Z) generated by generalized class transpositions. We show that the Kohlautomorphism of the group CT(Z) is induced by an inner automorphism of the group Sym(Z) and can be represented as the composition of two automorphisms of Sym(Z); namely, shift by and reflection with respect to 0. We suggest formulas for the action of these automorphisms onthe generators of ECT(Z).",
keywords = "Collatz problem, automorphism, class transposition, involution, permutation",
author = "Neshchadim, {M. V.} and Neshchadim, {S. M.}",
note = "The work was supported by the Russian Scientific Foundation (project no. 24-11-00119).",
year = "2025",
month = sep,
doi = "10.1134/S1055134425030058",
language = "English",
volume = "35",
pages = "221--228",
journal = "Siberian Advances in Mathematics",
issn = "1055-1344",
publisher = "Pleiades Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - The Group of Generalized Class Transpositions and its Automorphisms

AU - Neshchadim, M. V.

AU - Neshchadim, S. M.

N1 - The work was supported by the Russian Scientific Foundation (project no. 24-11-00119).

PY - 2025/9

Y1 - 2025/9

N2 - We introduce a group ECT(Z) generated by generalized class transpositions. We show that the Kohlautomorphism of the group CT(Z) is induced by an inner automorphism of the group Sym(Z) and can be represented as the composition of two automorphisms of Sym(Z); namely, shift by and reflection with respect to 0. We suggest formulas for the action of these automorphisms onthe generators of ECT(Z).

AB - We introduce a group ECT(Z) generated by generalized class transpositions. We show that the Kohlautomorphism of the group CT(Z) is induced by an inner automorphism of the group Sym(Z) and can be represented as the composition of two automorphisms of Sym(Z); namely, shift by and reflection with respect to 0. We suggest formulas for the action of these automorphisms onthe generators of ECT(Z).

KW - Collatz problem

KW - automorphism

KW - class transposition

KW - involution

KW - permutation

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105018722848&origin=inward

UR - https://www.mendeley.com/catalogue/08937710-b41b-30da-bbd4-853878ce6e18/

U2 - 10.1134/S1055134425030058

DO - 10.1134/S1055134425030058

M3 - Article

VL - 35

SP - 221

EP - 228

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 3

ER -

ID: 71020638