TY - JOUR

T1 - The Isomorphism Problem for Generalized Baumslag–Solitar Groups with One Mobile Edge

AU - Dudkin, F. A.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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 π1(A) of some labeled graph A. This paper deals with the isomorphism problem for GBS groups, which is the problem of determining whether π1(A) ≅ π1(A) for two given labeled graphsA and B. We describe an algorithm that decides this problem for the case where one of the labeled graphs has a sole mobile edge.

AB - 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 π1(A) of some labeled graph A. This paper deals with the isomorphism problem for GBS groups, which is the problem of determining whether π1(A) ≅ π1(A) for two given labeled graphsA and B. We describe an algorithm that decides this problem for the case where one of the labeled graphs has a sole mobile edge.

KW - generalized Baumslag–Solitar group

KW - isomorphism problem

KW - labeled graph

KW - TREES

KW - generalized Baumslag-Solitar group

UR - http://www.scopus.com/inward/record.url?scp=85030854965&partnerID=8YFLogxK

U2 - 10.1007/s10469-017-9440-y

DO - 10.1007/s10469-017-9440-y

M3 - Article

AN - SCOPUS:85030854965

VL - 56

SP - 197

EP - 209

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 3

ER -