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Universal Equivalence of Generalized Baumslag–Solitar Groups. / Dudkin, F. A.
в: Algebra and Logic, Том 59, № 5, 01.11.2020, стр. 357-366.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Universal Equivalence of Generalized Baumslag–Solitar Groups
AU - Dudkin, F. A.
N1 - Funding Information: Supported by SB RAS Fundamental Research Program I.1.1, project No. 0314-2019-0001. Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - A finitely generated group acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag–Solitar group (a GBS group). Every GBS group is the fundamental group Π1(A) of a suitable labeled graph A. We prove that if A and B are labeled trees, then the groups Π1(A) and Π1(B) are universally equivalent iff Π1(A) and Π1(B) are embeddable into each other. An algorithm for verifying universal equivalence is pointed out. Moreover, we specify simple conditions for checking this criterion in the case where the centralizer dimension is equal to 3.
AB - A finitely generated group acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag–Solitar group (a GBS group). Every GBS group is the fundamental group Π1(A) of a suitable labeled graph A. We prove that if A and B are labeled trees, then the groups Π1(A) and Π1(B) are universally equivalent iff Π1(A) and Π1(B) are embeddable into each other. An algorithm for verifying universal equivalence is pointed out. Moreover, we specify simple conditions for checking this criterion in the case where the centralizer dimension is equal to 3.
KW - embedding of groups
KW - existential equivalence
KW - generalized Baumslag–Solitar group
KW - universal equivalence
UR - http://www.scopus.com/inward/record.url?scp=85096847064&partnerID=8YFLogxK
U2 - 10.1007/s10469-020-09609-5
DO - 10.1007/s10469-020-09609-5
M3 - Article
AN - SCOPUS:85096847064
VL - 59
SP - 357
EP - 366
JO - Algebra and Logic
JF - Algebra and Logic
SN - 0002-5232
IS - 5
ER -
ID: 26134335