Universal Equivalence of Generalized Baumslag–Solitar Groups Full article
| Journal |
Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302 |
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| Output data | Year: 2020, Volume: 59, Number: 5, Pages: 357–366 Pages count : DOI: 10.1007/s10469-020-09609-5 | ||||
| Tags | generalized Baumslag–Solitar group, universal equivalence, existential equivalence, embedding of groups | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | 0314-2019-0001 |
Abstract:
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( ) of a suitable labeled graph . We prove that if and are labeled trees, then the groups π1( ) and π1( ) are universally equivalent iff π1( ) and π1( ) 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.
Cite:
Dudkin F.A.
Universal Equivalence of Generalized Baumslag–Solitar Groups
Algebra and Logic. 2020. V.59. N5. P.357–366. DOI: 10.1007/s10469-020-09609-5 WOS Scopus РИНЦ OpenAlex
Universal Equivalence of Generalized Baumslag–Solitar Groups
Algebra and Logic. 2020. V.59. N5. P.357–366. DOI: 10.1007/s10469-020-09609-5 WOS Scopus РИНЦ OpenAlex
Original:
Дудкин Ф.А.
Об универсальной эквивалентности обобщенных групп Баумслага–Солитера
Алгебра и логика. 2020. Т.59. №5. С.529-541. DOI: 10.33048/alglog.2020.59.502 РИНЦ OpenAlex
Об универсальной эквивалентности обобщенных групп Баумслага–Солитера
Алгебра и логика. 2020. Т.59. №5. С.529-541. DOI: 10.33048/alglog.2020.59.502 РИНЦ OpenAlex
Dates:
| Published print: | Nov 29, 2020 |
Identifiers:
| Web of science: | WOS:000593834300006 |
| Scopus: | 2-s2.0-85096847064 |
| Elibrary: | 45147700 |
| OpenAlex: | W3107231067 |