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

^*Corresponding author for this work

Mathematics

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 (US)
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 - May 15 2017

Funding

Keywords

Invariable generation
Thompson groups

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jalgebra.2017.01.019

Cite this

@article{36fe620d4bdc46dca40ceb699aa1adc9,

title = "Invariable generation of Thompson groups",

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.",

keywords = "Invariable generation, Thompson groups",

author = "Tsachik Gelander and Gili Golan and Kate Juschenko",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = may,

day = "15",

doi = "10.1016/j.jalgebra.2017.01.019",

language = "English (US)",

volume = "478",

pages = "261--270",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Invariable generation of Thompson groups

AU - Gelander, Tsachik

AU - Golan, Gili

AU - Juschenko, Kate

PY - 2017/5/15

Y1 - 2017/5/15

N2 - 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.

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.

KW - Invariable generation

KW - Thompson groups

UR - http://www.scopus.com/inward/record.url?scp=85010878041&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010878041&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2017.01.019

DO - 10.1016/j.jalgebra.2017.01.019

M3 - Article

AN - SCOPUS:85010878041

SN - 0021-8693

VL - 478

SP - 261

EP - 270

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Invariable generation of Thompson groups

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this