Geodesic
The isomorphism problem for generalized Baumslag–Solitar groups with one mobile edge
Algebra i logika, Tome 56 (2017) no. 3, pp. 300-316

Voir la notice de l'article provenant de la source Math-Net.Ru

A generalized Baumslag–Solitar group ($GBS$ group) is a finitely generated group $G$ which acts on a tree with all edge and vertex stabilizers infinite cyclic. Every $GBS$ group is the fundamental group $\pi_1(\mathbb A)$ of some graph labeled $\mathbb A$. This paper deals with the isomorphism problem for $GBS$ groups, which is the problem of determining whether $\pi_1(\mathbb A)\cong\pi_1(\mathbb B)$ for two given graphs labeled $\mathbb A$ and $\mathbb B$. We describe an algorithm that decides this problem for the case where one of the labeled graphs has one mobile edge.
Keywords: isomorphism problem, generalized Baumslag–Solitar group, labeled graph. 
@article{AL_2017_56_3_a1,
     author = {F. A. Dudkin},
     title = {The isomorphism problem for generalized {Baumslag{\textendash}Solitar} groups with one mobile edge},
     journal = {Algebra i logika},
     pages = {300--316},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_3_a1/}
}
TY  - JOUR
AU  - F. A. Dudkin
TI  - The isomorphism problem for generalized Baumslag–Solitar groups with one mobile edge
JO  - Algebra i logika
PY  - 2017
SP  - 300
EP  - 316
VL  - 56
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2017_56_3_a1/
LA  - ru
ID  - AL_2017_56_3_a1
ER  - 
%0 Journal Article
%A F. A. Dudkin
%T The isomorphism problem for generalized Baumslag–Solitar groups with one mobile edge
%J Algebra i logika
%D 2017
%P 300-316
%V 56
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2017_56_3_a1/
%G ru
%F AL_2017_56_3_a1
F. A. Dudkin. The isomorphism problem for generalized Baumslag–Solitar groups with one mobile edge. Algebra i logika, Tome 56 (2017) no. 3, pp. 300-316. http://geodesic.mathdoc.fr/item/AL_2017_56_3_a1/