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NECESSARY CONDITION FOR ISOMORPHISM OF GBS(n,1) GROUPS WITH NON-TRIVIAL CENTER. / Dudkin, F. A.

In: Siberian Electronic Mathematical Reports, Vol. 22, No. 2, 27.11.2025, p. 1401-1407.

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

Harvard

Dudkin, FA 2025, 'NECESSARY CONDITION FOR ISOMORPHISM OF GBS(n,1) GROUPS WITH NON-TRIVIAL CENTER', Siberian Electronic Mathematical Reports, vol. 22, no. 2, pp. 1401-1407. https://doi.org/10.33048/semi.2025.22.085

APA

Dudkin, F. A. (2025). NECESSARY CONDITION FOR ISOMORPHISM OF GBS(n,1) GROUPS WITH NON-TRIVIAL CENTER. Siberian Electronic Mathematical Reports, 22(2), 1401-1407. https://doi.org/10.33048/semi.2025.22.085

Vancouver

Dudkin FA. NECESSARY CONDITION FOR ISOMORPHISM OF GBS(n,1) GROUPS WITH NON-TRIVIAL CENTER. Siberian Electronic Mathematical Reports. 2025 Nov 27;22(2):1401-1407. doi: 10.33048/semi.2025.22.085

Author

Dudkin, F. A. / NECESSARY CONDITION FOR ISOMORPHISM OF GBS(n,1) GROUPS WITH NON-TRIVIAL CENTER. In: Siberian Electronic Mathematical Reports. 2025 ; Vol. 22, No. 2. pp. 1401-1407.

BibTeX

@article{3d036ae2fe8f48bda5290702d966275a,
title = "NECESSARY CONDITION FOR ISOMORPHISM OF GBS(n,1) GROUPS WITH NON-TRIVIAL CENTER",
abstract = "A finitely generated group Gn that acts on a tree T such that all edge stabilizers are infinite cyclic groups and all vertex stabilizers are free Abelian groups of rank n will be called a generalized Baumslag–Solitar group of type (n,1) (GBS(n,1) group). In this paper we find a criterion for such groups to have a non-trivial center and prove that if n ≥ 3 and two such groups with non-trivial center are isomorphic, then the corresponding GBS(1,1) groups must also be isomorphic.",
keywords = "generalized Baumslag–Solitar group, group with non-trivial center, isomorphism problem",
author = "Dudkin, {F. A.}",
note = "Dudkin, F.A. Necessary condition for isomorphism of GBS(n,1) groups with non-trivial center. Siberian Electronic Mathematical Reports. Vol. 22, No. 2, pp. 1401–1407 (2025). https://doi.org/10.33048/semi.2025.22.085 The work was supported by Russian Science Foundation (project 24-21-00214), https://rscf.ru/project/24-21-00214/.",
year = "2025",
month = nov,
day = "27",
doi = "10.33048/semi.2025.22.085",
language = "English",
volume = "22",
pages = "1401--1407",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "2",

}

RIS

TY - JOUR

T1 - NECESSARY CONDITION FOR ISOMORPHISM OF GBS(n,1) GROUPS WITH NON-TRIVIAL CENTER

AU - Dudkin, F. A.

N1 - Dudkin, F.A. Necessary condition for isomorphism of GBS(n,1) groups with non-trivial center. Siberian Electronic Mathematical Reports. Vol. 22, No. 2, pp. 1401–1407 (2025). https://doi.org/10.33048/semi.2025.22.085 The work was supported by Russian Science Foundation (project 24-21-00214), https://rscf.ru/project/24-21-00214/.

PY - 2025/11/27

Y1 - 2025/11/27

N2 - A finitely generated group Gn that acts on a tree T such that all edge stabilizers are infinite cyclic groups and all vertex stabilizers are free Abelian groups of rank n will be called a generalized Baumslag–Solitar group of type (n,1) (GBS(n,1) group). In this paper we find a criterion for such groups to have a non-trivial center and prove that if n ≥ 3 and two such groups with non-trivial center are isomorphic, then the corresponding GBS(1,1) groups must also be isomorphic.

AB - A finitely generated group Gn that acts on a tree T such that all edge stabilizers are infinite cyclic groups and all vertex stabilizers are free Abelian groups of rank n will be called a generalized Baumslag–Solitar group of type (n,1) (GBS(n,1) group). In this paper we find a criterion for such groups to have a non-trivial center and prove that if n ≥ 3 and two such groups with non-trivial center are isomorphic, then the corresponding GBS(1,1) groups must also be isomorphic.

KW - generalized Baumslag–Solitar group

KW - group with non-trivial center

KW - isomorphism problem

UR - https://www.mendeley.com/catalogue/3602632c-208c-336f-b9fe-24096581d06c/

UR - https://www.scopus.com/pages/publications/105024896669

U2 - 10.33048/semi.2025.22.085

DO - 10.33048/semi.2025.22.085

M3 - Article

VL - 22

SP - 1401

EP - 1407

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

ER -

ID: 72844460