An infinitude of counterexamples to Herzog’s conjecture on involutions in simple groups

Chimere Stanley Anabanti; Stefan Hammer; Nneka Chigozie Okoli

doi:10.1080/00927872.2020.1836563

An infinitude of counterexamples to Herzog’s conjecture on involutions in simple groups

Chimere Stanley Anabanti^*, Stefan Hammer, Nneka Chigozie Okoli

^*Corresponding author for this work

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

Abstract

In 1979, Herzog conjectured that two finite simple groups containing the same number of involutions have the same order. Zarrin, in a 2018 published paper, disproved Herzog’s conjecture with a counterexample. The goal of this article is to prove that there are infinitely many counterexamples to Herzog’s conjecture. In doing so, we obtain an explicit formula for the number of involutions in the groups involved.

Original language	English
Pages (from-to)	1415-1421
Number of pages	7
Journal	Communications in Algebra
Volume	49
Issue number	4
Early online date	29 Oct 2020
DOIs	https://doi.org/10.1080/00927872.2020.1836563
Publication status	Published - 2021

Keywords

Elements of odd prime order
finite simple groups
involutions

ASJC Scopus subject areas

Algebra and Number Theory

Fields of Expertise

Information, Communication & Computing

Access to Document

10.1080/00927872.2020.1836563Licence: CC BY-NC-ND 4.0

Cite this

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title = "An infinitude of counterexamples to Herzog{\textquoteright}s conjecture on involutions in simple groups",

abstract = "In 1979, Herzog conjectured that two finite simple groups containing the same number of involutions have the same order. Zarrin, in a 2018 published paper, disproved Herzog{\textquoteright}s conjecture with a counterexample. The goal of this article is to prove that there are infinitely many counterexamples to Herzog{\textquoteright}s conjecture. In doing so, we obtain an explicit formula for the number of involutions in the groups involved.",

keywords = "Elements of odd prime order, finite simple groups, involutions",

author = "Anabanti, {Chimere Stanley} and Stefan Hammer and Okoli, {Nneka Chigozie}",

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journal = "Communications in Algebra",

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AU - Anabanti, Chimere Stanley

AU - Hammer, Stefan

AU - Okoli, Nneka Chigozie

PY - 2021

Y1 - 2021

N2 - In 1979, Herzog conjectured that two finite simple groups containing the same number of involutions have the same order. Zarrin, in a 2018 published paper, disproved Herzog’s conjecture with a counterexample. The goal of this article is to prove that there are infinitely many counterexamples to Herzog’s conjecture. In doing so, we obtain an explicit formula for the number of involutions in the groups involved.

AB - In 1979, Herzog conjectured that two finite simple groups containing the same number of involutions have the same order. Zarrin, in a 2018 published paper, disproved Herzog’s conjecture with a counterexample. The goal of this article is to prove that there are infinitely many counterexamples to Herzog’s conjecture. In doing so, we obtain an explicit formula for the number of involutions in the groups involved.

KW - Elements of odd prime order

KW - finite simple groups

KW - involutions

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U2 - 10.1080/00927872.2020.1836563

DO - 10.1080/00927872.2020.1836563

M3 - Article

SN - 0092-7872

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JO - Communications in Algebra

JF - Communications in Algebra

IS - 4

ER -

An infinitude of counterexamples to Herzog’s conjecture on involutions in simple groups

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

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Doctoral Program: Discrete Mathematics

Cite this

An infinitude of counterexamples to Herzog’s conjecture on involutions in simple groups

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

Other files and links

Fingerprint

Projects

Doctoral Program: Discrete Mathematics

Cite this