On (2,3)-generation of Fischer's largest sporadic simple group $ F{i}_{24}^{\phantom{\rule{0.2em}{0ex}}\prime }$

Faryad Ali; Mohammed Ali Faya Ibrahim; Andrew Woldar

doi:10.1016/j.crma.2019.05.004

Combinatorics/Algebra

On (2,3)-generation of Fischer's largest sporadic simple group

F i_{24}^{'}

[Sur la (2,3)-génération du plus grand groupe simple sporadique de Fischer

F i_{24}^{'}

]

Présenté par : the Editorial Board

Faryad Ali ¹ ; Mohammed Ali Faya Ibrahim ² ; Andrew Woldar ³

¹ Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O.Box 90950, Riyadh 11623, Saudi Arabia
² Department of Mathematics, Najran University, Najran, Saudi Arabia
³ Department of Mathematics and Statistics, Villanova University, Villanova, PA 19085, USA

Comptes Rendus. Mathématique, Volume 357 (2019) no. 5, pp. 401-412.

Résumé
Abstract

Un groupe G est dit $(2, 3)$ -engendré s'il peut être engendré par une involution x et un élément y d'ordre trois. Pour un groupe simple sporadique G, il a été montré par le troisième auteur Woldar (1989) [26] que G est $(2, 3)$ -engendré si et seulement si $G \notin {M_{11}, M_{22}, M_{23}, M c L}$ . Nous étudions ici toutes les $(2, 3)$ -générations du plus grand groupe simple sporadique de Fischer $F i_{24}^{'}$ , en supposant que le produit xy est d'ordre premier.

A group G is said to be $(2, 3)$ -generated if it can be generated by an involution x and an element y of order three. For G a sporadic simple group, it was proved by the third author Woldar (1989) [26] that G is $(2, 3)$ -generated if and only if $G \notin {M_{11}, M_{22}, M_{23}, M c L}$ . In this paper, we investigate all possible $(2, 3)$ -generations of Fischer's largest sporadic simple group $F i_{24}^{'}$ under the assumption that the product xy has prime order.

Reçu le : 2018-12-15
Accepté le : 2019-05-16
Publié le : 2019-05-01

DOI : 10.1016/j.crma.2019.05.004

Affiliations des auteurs :

Faryad Ali ¹ ; Mohammed Ali Faya Ibrahim ² ; Andrew Woldar ³

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     title = {On (2,3)-generation of {Fischer's} largest sporadic simple group $ F{i}_{24}^{\phantom{\rule{0.2em}{0ex}}\prime }$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {401--412},
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     year = {2019},
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Faryad Ali; Mohammed Ali Faya Ibrahim; Andrew Woldar. On (2,3)-generation of Fischer's largest sporadic simple group $ F{i}_{24}^{\phantom{\rule{0.2em}{0ex}}\prime }$. Comptes Rendus. Mathématique, Volume 357 (2019) no. 5, pp. 401-412. doi : 10.1016/j.crma.2019.05.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.05.004/

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Cité par Sources :

^☆ This work was funded by the National Plan for Science, Technology and Innovation (MARRIFAH) - King Abdulaziz City for Science and Technology - Kingdom of Saudi Arabia, award number (13-MAT264-08).

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