Influence of the number of Sylow subgroups on solvability of finite groups

Chimere Stanley Anabanti; Alexander Moretó; Mohammad Zarrin

doi:10.5802/crmath.146

Théorie des groupes

Influence of the number of Sylow subgroups on solvability of finite groups

Chimere Stanley Anabanti ¹ ; Alexander Moretó ² ; Mohammad Zarrin ³

¹ Institut für Analysis und Zahlentheorie, Technische Universität Graz (TU Graz), Graz 8010 Austria.
² Departament de Matemàtiques, Universitat de València, 46100, Burjassot, València Spain.
³ Department of Mathematics, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran.

Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1227-1230.

Résumé

Let $G$ be a finite group. We prove that if the number of Sylow $3$ -subgroups of $G$ is at most $7$ and the number of Sylow $5$ -subgroups of $G$ is at most $1455$ , then $G$ is solvable. This is a strong form of a recent conjecture of Robati.

Reçu le : 2020-10-04
Révisé le : 2020-11-05
Accepté le : 2020-11-05
Publié le : 2021-01-25

DOI : 10.5802/crmath.146

Classification : 20D10, 20D20, 20F16, 20F19

Affiliations des auteurs :

Chimere Stanley Anabanti ¹ ; Alexander Moretó ² ; Mohammad Zarrin ³

¹ Institut für Analysis und Zahlentheorie, Technische Universität Graz (TU Graz), Graz 8010 Austria.
² Departament de Matemàtiques, Universitat de València, 46100, Burjassot, València Spain.
³ Department of Mathematics, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran.

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Chimere Stanley Anabanti and Alexander Moret\'o and Mohammad Zarrin},
     title = {Influence of the number of {Sylow} subgroups on solvability of finite groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1227--1230},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {11-12},
     year = {2020},
     doi = {10.5802/crmath.146},
     language = {en},
}

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Chimere Stanley Anabanti; Alexander Moretó; Mohammad Zarrin. Influence of the number of Sylow subgroups on solvability of finite groups. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1227-1230. doi : 10.5802/crmath.146. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.146/

Bibliographie
Cité par

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