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

^*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	englisch
Seiten (von - bis)	1415-1421
Seitenumfang	7
Fachzeitschrift	Communications in Algebra
Jahrgang	49
Ausgabenummer	4
Frühes Online-Datum	29 Okt. 2020
DOIs	https://doi.org/10.1080/00927872.2020.1836563
Publikationsstatus	Veröffentlicht - 2021

ASJC Scopus subject areas

Algebra und Zahlentheorie

Fields of Expertise

Information, Communication & Computing

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

Andere Dateien und Links

http://www.scopus.com/inward/record.url?scp=85094922202&partnerID=8YFLogxK

DK Diskrete Mathematik
Ebner, O., Lehner, F., Greinecker, F., Burkard, R., Wallner, J., Elsholtz, C., Woess, W., Raseta, M., Bazarova, A., Krenn, D., Lehner, F., Kang, M., Tichy, R., Sava-Huss, E., Klinz, B., Heuberger, C., Grabner, P., Barroero, F., Cuno, J., Kreso, D., Berkes, I. & Kerber, M.
1/05/10 → 30/06/24
Projekt: Forschungsprojekt

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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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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

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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

ASJC Scopus subject areas

Fields of Expertise

Zugriff auf Dokument

Andere Dateien und Links

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Projekte

DK Diskrete Mathematik

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