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Notes on the average number of Sylow subgroups of finite groups

Jiakuan Lu; Wei Meng; Alexander Moretó; Kaisun Wu — 2021

Czechoslovak Mathematical Journal

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 $G / F (G) ≅ A_{5}$ . This generalizes an earlier result by the third author.

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