no. 11-12
Théorie des groupes
Influence of the number of Sylow subgroups on solvability of finite groups
Anabanti, Chimere Stanley1 ; Moretó, Alexander2  ; Zarrin, Mohammad3
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, Tome 358 (2020) no. 11-12, pp. 1227-1230.

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.

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DOI : 10.5802/crmath.146
Classification : 20D10, 20D20, 20F16, 20F19
Anabanti, Chimere Stanley 1 ; Moretó, Alexander 2 ; Zarrin, Mohammad 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. 
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Anabanti, Chimere Stanley; Moretó, Alexander; Zarrin, Mohammad. Influence of the number of Sylow subgroups on solvability of finite groups. Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1227-1230. doi : 10.5802/crmath.146. http://www.numdam.org/articles/10.5802/crmath.146/

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