Fraïssé limits of limit groups

Olga Kharlampovich; Alexei Myasnikov; Rizos Sklinos

doi:10.1016/j.jalgebra.2019.08.003

Fraïssé limits of limit groups

Olga Kharlampovich
, Alexei Myasnikov
, Rizos Sklinos

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We modify the notion of a Fraïssé class and show that various interesting classes of groups, notably the class of nonabelian limit groups and the class of finitely generated elementary free groups, admit Fraïssé limits. Furthermore, we rediscover Lyndon's Z[t]-exponential completions of countable torsion-free CSA groups, as Fraïssé limits with respect to extensions of centralizers.

Original language	English
Pages (from-to)	300-323
Number of pages	24
Journal	Journal of Algebra
Volume	545
DOIs	https://doi.org/10.1016/j.jalgebra.2019.08.003
State	Published - 1 Mar 2020

Keywords

Fraïssé limit
Free group
Limit group
Lyndon exponential group

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10.1016/j.jalgebra.2019.08.003

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abstract = "We modify the notion of a Fra{\"i}ss{\'e} class and show that various interesting classes of groups, notably the class of nonabelian limit groups and the class of finitely generated elementary free groups, admit Fra{\"i}ss{\'e} limits. Furthermore, we rediscover Lyndon's Z[t]-exponential completions of countable torsion-free CSA groups, as Fra{\"i}ss{\'e} limits with respect to extensions of centralizers.",

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author = "Olga Kharlampovich and Alexei Myasnikov and Rizos Sklinos",

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T1 - Fraïssé limits of limit groups

AU - Kharlampovich, Olga

AU - Myasnikov, Alexei

AU - Sklinos, Rizos

PY - 2020/3/1

Y1 - 2020/3/1

N2 - We modify the notion of a Fraïssé class and show that various interesting classes of groups, notably the class of nonabelian limit groups and the class of finitely generated elementary free groups, admit Fraïssé limits. Furthermore, we rediscover Lyndon's Z[t]-exponential completions of countable torsion-free CSA groups, as Fraïssé limits with respect to extensions of centralizers.

AB - We modify the notion of a Fraïssé class and show that various interesting classes of groups, notably the class of nonabelian limit groups and the class of finitely generated elementary free groups, admit Fraïssé limits. Furthermore, we rediscover Lyndon's Z[t]-exponential completions of countable torsion-free CSA groups, as Fraïssé limits with respect to extensions of centralizers.

KW - Fraïssé limit

KW - Free group

KW - Limit group

KW - Lyndon exponential group

UR - https://www.scopus.com/pages/publications/85070699840

UR - https://www.scopus.com/pages/publications/85070699840#tab=citedBy

U2 - 10.1016/j.jalgebra.2019.08.003

DO - 10.1016/j.jalgebra.2019.08.003

M3 - Article

AN - SCOPUS:85070699840

SN - 0021-8693

VL - 545

SP - 300

EP - 323

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Fraïssé limits of limit groups

Abstract

Keywords

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