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 -