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Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups Full article

Journal Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260
Output data Year: 2025, Volume: 66, Number: 4, Pages: 946-951 Pages count : 6 DOI: 10.1134/s003744662504007x
Tags generalized Baumslag–Solitar group, Hopfian group, vertex-transitive action
Authors Guskov N.V. 1 , Dudkin F.A. 2
Affiliations
1 Novosibirsk State University
2 Sobolev Institute of Mathematics

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0002

Abstract: A generalized Baumslag–Solitar group (GBS group) is a finitely generated group G acting on a tree in such a way that all vertex and edge stabilizers are infinite cyclic groups. If G 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.
Cite: Guskov N.V. , Dudkin F.A.
Hopficity of Vertex-Transitive Generalized Baumslag–Solitar Groups
Siberian Mathematical Journal. 2025. V.66. N4. P.946-951. DOI: 10.1134/s003744662504007x WOS Scopus РИНЦ OpenAlex
Original: Гуськов Н.В. , Дудкин Ф.А.
Хопфовость вершинно-транзитивных обобщенных групп Баумслага–Солитера
Сибирский математический журнал. 2025. Т.66. №4. С.635-642. DOI: 10.33048/smzh.2025.66.407 РИНЦ
Dates:
Submitted: Dec 18, 2024
Accepted: May 26, 2025
Published print: Jul 23, 2025
Published online: Jul 23, 2025
Identifiers:
Web of science: WOS:001535187000010
Scopus: 2-s2.0-105011278921
Elibrary: 82650978
OpenAlex: W4412610040
Citing: Пока нет цитирований
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