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Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups. / Guskov, N. V.; Dudkin, F. A.

в: Siberian Mathematical Journal, Том 66, № 4, 23.07.2025, стр. 946-951.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Guskov, NV & Dudkin, FA 2025, 'Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups', Siberian Mathematical Journal, Том. 66, № 4, стр. 946-951. https://doi.org/10.1134/S003744662504007X

APA

Guskov, N. V., & Dudkin, F. A. (2025). Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups. Siberian Mathematical Journal, 66(4), 946-951. https://doi.org/10.1134/S003744662504007X

Vancouver

Guskov NV, Dudkin FA. Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups. Siberian Mathematical Journal. 2025 июль 23;66(4):946-951. doi: 10.1134/S003744662504007X

Author

Guskov, N. V. ; Dudkin, F. A. / Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups. в: Siberian Mathematical Journal. 2025 ; Том 66, № 4. стр. 946-951.

BibTeX

@article{38c80b78af88417a9ae4370a2f974b82,
title = "Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups",
abstract = "A generalized Baumslag–Solitar group (GBS group) is a finitely generated group acting on a tree in such a way that all vertex and edge stabilizers are infinite cyclic groups.If acts transitively on the set of vertices, we refer to it as a vertex-transitive GBS group (VTGBS group).A group is said to be Hopfian if every epimorphism from the group onto itself is an isomorphism.In this paper, we obtain several sufficient conditions for VTGBS groups to be non-Hopfian and describe epimorphisms of such groups.",
keywords = "512.54, Hopfian group, generalized Baumslag–Solitar group, vertex-transitive action",
author = "Guskov, {N. V.} and Dudkin, {F. A.}",
note = "The work of Dudkin was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0002) (Theorem 1). Guskov, N. V. Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups / N. V. Guskov, F. A. Dudkin // Siberian Mathematical Journal. – 2025. – Vol. 66, No. 4. – P. 946-951. – DOI 10.1134/S003744662504007X. ",
year = "2025",
month = jul,
day = "23",
doi = "10.1134/S003744662504007X",
language = "English",
volume = "66",
pages = "946--951",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "Pleiades Publishing",
number = "4",

}

RIS

TY - JOUR

T1 - Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups

AU - Guskov, N. V.

AU - Dudkin, F. A.

N1 - The work of Dudkin was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0002) (Theorem 1). Guskov, N. V. Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups / N. V. Guskov, F. A. Dudkin // Siberian Mathematical Journal. – 2025. – Vol. 66, No. 4. – P. 946-951. – DOI 10.1134/S003744662504007X.

PY - 2025/7/23

Y1 - 2025/7/23

N2 - A generalized Baumslag–Solitar group (GBS group) is a finitely generated group acting on a tree in such a way that all vertex and edge stabilizers are infinite cyclic groups.If acts transitively on the set of vertices, we refer to it as a vertex-transitive GBS group (VTGBS group).A group is said to be Hopfian if every epimorphism from the group onto itself is an isomorphism.In this paper, we obtain several sufficient conditions for VTGBS groups to be non-Hopfian and describe epimorphisms of such groups.

AB - A generalized Baumslag–Solitar group (GBS group) is a finitely generated group acting on a tree in such a way that all vertex and edge stabilizers are infinite cyclic groups.If acts transitively on the set of vertices, we refer to it as a vertex-transitive GBS group (VTGBS group).A group is said to be Hopfian if every epimorphism from the group onto itself is an isomorphism.In this paper, we obtain several sufficient conditions for VTGBS groups to be non-Hopfian and describe epimorphisms of such groups.

KW - 512.54

KW - Hopfian group

KW - generalized Baumslag–Solitar group

KW - vertex-transitive action

UR - https://www.mendeley.com/catalogue/a8e00f33-68f8-3406-956a-92304063d496/

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105011278921&origin=inward

UR - https://www.elibrary.ru/item.asp?id=82650978

U2 - 10.1134/S003744662504007X

DO - 10.1134/S003744662504007X

M3 - Article

VL - 66

SP - 946

EP - 951

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -

ID: 68585631