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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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

Keywords

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

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2025.03.020

Cite this

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title = "Automorphisms of the Rado meet-tree",

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.",

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

author = "Itay Kaplan and Binyamin Riahi and \{Rodr{\'i}guez Fanlo\}, Arturo",

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year = "2025",

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doi = "10.1016/j.jalgebra.2025.03.020",

language = "الإنجليزيّة",

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T1 - Automorphisms of the Rado meet-tree

AU - Kaplan, Itay

AU - Riahi, Binyamin

AU - Rodríguez Fanlo, Arturo

PY - 2025/9/1

Y1 - 2025/9/1

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 - http://www.scopus.com/inward/record.url?scp=105002019564&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2025.03.020

DO - 10.1016/j.jalgebra.2025.03.020

M3 - مقالة

SN - 0021-8693

VL - 677

SP - 13

EP - 60

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Automorphisms of the Rado meet-tree

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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