Invariable generation of Thompson groups

Tsachik Gelander; Gili Golan; Kate Juschenko

doi:10.1016/j.jalgebra.2017.01.019

Invariable generation of Thompson groups

Tsachik Gelander, Gili Golan, Kate Juschenko

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

11 Scopus citations

Abstract

A subset S of a group G invariably generates G if G=〈s^g(s)|s∈S〉 for every choice of g(s)∈G,s∈S. We say that a group G is invariably generated if such S exists, or equivalently, if S=G invariably generates G. In this paper, we study invariable generation of Thompson groups. We show that Thompson group F is invariably generated by a finite set, whereas Thompson groups T and V are not invariably generated.

Original language	English
Pages (from-to)	261-270
Number of pages	10
Journal	Journal of Algebra
Volume	478
DOIs	https://doi.org/10.1016/j.jalgebra.2017.01.019
State	Published - 15 May 2017
Externally published	Yes

Keywords

Invariable generation
Thompson groups

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2017.01.019

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abstract = "A subset S of a group G invariably generates G if G=〈sg(s)|s∈S〉 for every choice of g(s)∈G,s∈S. We say that a group G is invariably generated if such S exists, or equivalently, if S=G invariably generates G. In this paper, we study invariable generation of Thompson groups. We show that Thompson group F is invariably generated by a finite set, whereas Thompson groups T and V are not invariably generated.",

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AB - A subset S of a group G invariably generates G if G=〈sg(s)|s∈S〉 for every choice of g(s)∈G,s∈S. We say that a group G is invariably generated if such S exists, or equivalently, if S=G invariably generates G. In this paper, we study invariable generation of Thompson groups. We show that Thompson group F is invariably generated by a finite set, whereas Thompson groups T and V are not invariably generated.

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Invariable generation of Thompson groups

Abstract

Keywords

ASJC Scopus subject areas

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