Czechoslovak Mathematical Journal, Vol. 71, No. 4, pp. 1129-1132, 2021
Notes on the average number of Sylow subgroups of finite groups
Jiakuan Lu, Wei Meng, Alexander Moretó, Kaisun Wu
Received June 4, 2020. Published online March 19, 2021.
Abstract: We show that if the average number of (nonnormal) Sylow subgroups of a finite group is less than $\frac{29}4$ then $G$ is solvable or $G/F(G)\cong A_5$. This generalizes an earlier result by the third author.
Affiliations: Jiakuan Lu (corresponding author), School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, Guangxi, P. R. China, e-mail: jklu@gxnu.edu.cn; Wei Meng, School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541006, Guangxi, P. R. China, e-mail: mlwhappyhappy@163.com; Alexander Moretó, Departament de Matemàtiques,Universitat de València, 46100 Burjassot, València, Spain; e-mail: Alexander.Moreto@uv.es; Kaisun Wu, School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, Guangxi, P. R. China, e-mail: 1547049416@qq.com