Automorphisms of the Rado meet-tree

Itay Kaplan; Binyamin Riahi; Arturo Rodríguez Fanlo

doi:10.1016/j.jalgebra.2025.03.020

Automorphisms of the Rado meet-tree

Itay Kaplan
, Binyamin Riahi
, Arturo Rodríguez Fanlo^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

1 Scopus citations

Abstract

We prove that the group of automorphisms of the generic meet-tree expansion of an infinite non-unary free Fraïssé limit over a finite relational language is simple. As a prototypical case, the group of automorphisms of the Rado meet-tree (i.e. the Fraïssé limit of finite graphs which are also meet-trees) is simple.

Original language	English
Pages (from-to)	13-60
Number of pages	48
Journal	Journal of Algebra
Volume	677
DOIs	https://doi.org/10.1016/j.jalgebra.2025.03.020
State	Published - 1 Sep 2025

Bibliographical note

Publisher Copyright:
© 2025 Elsevier Inc.

Keywords

Automorphism groups
Fraisse limits
Homogeneous structures
Meet-trees
Oligomorphic permutation groups
Semilattices
Simple groups
Stationary independence relations

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10.1016/j.jalgebra.2025.03.020

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abstract = "We prove that the group of automorphisms of the generic meet-tree expansion of an infinite non-unary free Fra{\"i}ss{\'e} limit over a finite relational language is simple. As a prototypical case, the group of automorphisms of the Rado meet-tree (i.e. the Fra{\"i}ss{\'e} limit of finite graphs which are also meet-trees) is simple.",

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AU - Riahi, Binyamin

AU - Rodríguez Fanlo, Arturo

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N2 - We prove that the group of automorphisms of the generic meet-tree expansion of an infinite non-unary free Fraïssé limit over a finite relational language is simple. As a prototypical case, the group of automorphisms of the Rado meet-tree (i.e. the Fraïssé limit of finite graphs which are also meet-trees) is simple.

AB - We prove that the group of automorphisms of the generic meet-tree expansion of an infinite non-unary free Fraïssé limit over a finite relational language is simple. As a prototypical case, the group of automorphisms of the Rado meet-tree (i.e. the Fraïssé limit of finite graphs which are also meet-trees) is simple.

KW - Automorphism groups

KW - Fraisse limits

KW - Homogeneous structures

KW - Meet-trees

KW - Oligomorphic permutation groups

KW - Semilattices

KW - Simple groups

KW - Stationary independence relations

UR - https://www.scopus.com/pages/publications/105002019564

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VL - 677

SP - 13

EP - 60

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Automorphisms of the Rado meet-tree

Abstract

Bibliographical note

Keywords

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