Highly transitive actions of Out(Fn)

Shelly Garion; Yair Glasner

doi:10.4171/GGD/185

Highly transitive actions of Out(Fn)

Shelly Garion
, Yair Glasner

Department of Mathematics

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

13 Scopus citations

Abstract

An action of a group on a set is called k-transitive if it is transitive on ordered k-tuples and highly transitive if it is k-transitive for every k. We show that for n ≤ 4 the group Out(Fn) D Aut(Fn)=Inn(Fn) admits a faithful highly transitive action on a countable set.

Original language	English
Pages (from-to)	357-376
Number of pages	20
Journal	Groups, Geometry, and Dynamics
Volume	7
Issue number	2
DOIs	https://doi.org/10.4171/GGD/185
State	Published - 25 Oct 2013

Keywords

Free group
Highly transitive action
Outer automorphism group

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/GGD/185

Cite this

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title = "Highly transitive actions of Out(Fn)",

abstract = "An action of a group on a set is called k-transitive if it is transitive on ordered k-tuples and highly transitive if it is k-transitive for every k. We show that for n ≤ 4 the group Out(Fn) D Aut(Fn)=Inn(Fn) admits a faithful highly transitive action on a countable set.",

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author = "Shelly Garion and Yair Glasner",

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N2 - An action of a group on a set is called k-transitive if it is transitive on ordered k-tuples and highly transitive if it is k-transitive for every k. We show that for n ≤ 4 the group Out(Fn) D Aut(Fn)=Inn(Fn) admits a faithful highly transitive action on a countable set.

AB - An action of a group on a set is called k-transitive if it is transitive on ordered k-tuples and highly transitive if it is k-transitive for every k. We show that for n ≤ 4 the group Out(Fn) D Aut(Fn)=Inn(Fn) admits a faithful highly transitive action on a countable set.

KW - Free group

KW - Highly transitive action

KW - Outer automorphism group

UR - https://www.scopus.com/pages/publications/84886919323

U2 - 10.4171/GGD/185

DO - 10.4171/GGD/185

M3 - Article

AN - SCOPUS:84886919323

SN - 1661-7207

VL - 7

SP - 357

EP - 376

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 2

ER -

Highly transitive actions of Out(Fn)

Abstract

Keywords

ASJC Scopus subject areas

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