Generalised triangle groups of type (2,3,2) with no cyclic essential representations

James Howie; Olexandr Konovalov

doi:10.1515/9783111473574-002

Generalised triangle groups of type (2,3,2) with no cyclic essential representations

James Howie^*, Olexandr Konovalov

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

Abstract

A conjecture of Rosenberger asserts that every generalised triangle group either is virtually soluble or contains a non-abelian free subgroup. Modulo two exceptional cases, we verify this conjecture for generalised triangle groups of type (2,3,2) which do not admit essential representations onto the cyclic group of order 6.

Original language	English
Title of host publication	Finitely presented groups
Subtitle of host publication	with applications in post-quantum cryptography and artificial intelligence
Editors	Volker Diekert, Martin Kreuzer
Place of Publication	Berlin
Publisher	de Gruyter
Pages	27-42
ISBN (Electronic)	9783111473574, 9783111474274
ISBN (Print)	9783111473376
DOIs	https://doi.org/10.1515/9783111473574-002
Publication status	Accepted/In press - 26 Mar 2024

Keywords

Generalised triangle groups
Free subgroups
Tits alternative
Rosenberger conjecture
Essential representations
Trace polynomials
Small cancellation
Computational group theory

Access to Document

10.1515/9783111473574-002

Embargoed Document

Howie-2024-Generalised-triangle-groups-Ch-AAM-CCBY
Accepted author manuscript, 378 KB
Licence: CC BY
Embargo ends: 1/01/50

CoDiMa: CoDiMa (CCP in the area of Computational Discrete Mathematics)
Linton, S. A. (PI) & Konovalov, O. (CoI)
EPSRC
1/03/15 → 29/02/20
Project: Standard

Generalised triangle groups of type (2,3,2) with no cyclic essential representations. Supplementary code.
Howie, J. (Creator) & Konovalov, O. (Creator), Zenodo, 2 Mar 2024
DOI: 10.5281/zenodo.10401274, https://github.com/olexandr-konovalov/generalised-triangle-groups-232
Dataset: Software

Cite this

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title = "Generalised triangle groups of type (2,3,2) with no cyclic essential representations",

abstract = "A conjecture of Rosenberger asserts that every generalised triangle group either is virtually soluble or contains a non-abelian free subgroup. Modulo two exceptional cases, we verify this conjecture for generalised triangle groups of type (2,3,2) which do not admit essential representations onto the cyclic group of order 6.",

keywords = "Generalised triangle groups, Free subgroups, Tits alternative, Rosenberger conjecture, Essential representations, Trace polynomials, Small cancellation, Computational group theory",

author = "James Howie and Olexandr Konovalov",

note = "Funding: The authors are grateful to CCP-CoDiMa (Collaborative Computational Project in the area of Computational Discrete Mathematics, EPSRC grant EP/M022641/1) for support in the earlier stage of this project.",

year = "2024",

month = mar,

day = "26",

doi = "10.1515/9783111473574-002",

language = "English",

isbn = "9783111473376",

pages = "27--42",

editor = "Volker Diekert and Martin Kreuzer",

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Generalised triangle groups of type (2,3,2) with no cyclic essential representations. / Howie, James; Konovalov, Olexandr.
Finitely presented groups: with applications in post-quantum cryptography and artificial intelligence. ed. / Volker Diekert; Martin Kreuzer. Berlin: de Gruyter, 2024. p. 27-42.

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

TY - CHAP

T1 - Generalised triangle groups of type (2,3,2) with no cyclic essential representations

AU - Howie, James

AU - Konovalov, Olexandr

N1 - Funding: The authors are grateful to CCP-CoDiMa (Collaborative Computational Project in the area of Computational Discrete Mathematics, EPSRC grant EP/M022641/1) for support in the earlier stage of this project.

PY - 2024/3/26

Y1 - 2024/3/26

N2 - A conjecture of Rosenberger asserts that every generalised triangle group either is virtually soluble or contains a non-abelian free subgroup. Modulo two exceptional cases, we verify this conjecture for generalised triangle groups of type (2,3,2) which do not admit essential representations onto the cyclic group of order 6.

AB - A conjecture of Rosenberger asserts that every generalised triangle group either is virtually soluble or contains a non-abelian free subgroup. Modulo two exceptional cases, we verify this conjecture for generalised triangle groups of type (2,3,2) which do not admit essential representations onto the cyclic group of order 6.

KW - Generalised triangle groups

KW - Free subgroups

KW - Tits alternative

KW - Rosenberger conjecture

KW - Essential representations

KW - Trace polynomials

KW - Small cancellation

KW - Computational group theory

U2 - 10.1515/9783111473574-002

DO - 10.1515/9783111473574-002

M3 - Chapter (peer-reviewed)

SN - 9783111473376

SP - 27

EP - 42

BT - Finitely presented groups

A2 - Diekert, Volker

A2 - Kreuzer, Martin

PB - de Gruyter

CY - Berlin

ER -

Generalised triangle groups of type (2,3,2) with no cyclic essential representations

Abstract

Keywords

Access to Document

Embargoed Document

Fingerprint

Projects

CoDiMa: CoDiMa (CCP in the area of Computational Discrete Mathematics)

Datasets

Generalised triangle groups of type (2,3,2) with no cyclic essential representations. Supplementary code.

Cite this