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Rusong Yang, Kairan Yang and Rulin Shen, On the solvability of finite groups and the number of Sylow 2-subgroups, Eur. J. Math. Appl. 2 (2022), Article ID 3.

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Volume 2 (2022), Article ID 3

https://doi.org/10.28919/ejma.2022.2.3

Published: 11/01/2022

Abstract:

Let $G$ be a finite group. Denoted by $n_2(G)$ the number of Sylow $2$-subgroups of $G$. In this paper, we prove if $G$ is non-solvable and $n_2(G)$ is a power of a prime $p$, then $p$ is a Fermat prime.

How to Cite:

Rusong Yang, Kairan Yang and Rulin Shen, On the solvability of finite groups and the number of Sylow 2-subgroups, Eur. J. Math. Appl. 2 (2022), Article ID 3. https://doi.org/10.28919/ejma.2022.2.3