• A Note on 2-Nilpotence of Finite Groups

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/123/02/0235-0238

• # Keywords

Finite group; 2-nilpotent group; quaternion-free.

• # Abstract

Ballester-Bolinches and Guo showed that a finite group 𝐺 is 2-nilpotent if 𝐺 satisfies: (1) a Sylow 2-subgroup 𝑃 of 𝐺 is quaternion-free and (2) $\Omega_1(P\cap G')\leq Z(P)$ and $N_G(P)$ is 2-nilpotent. In this paper, it is obtained that 𝐺 is a non-2-nilpotent group of order $16q$ for an odd prime 𝑞 satisfying (1) a Sylow 2-subgroup 𝑃 of 𝐺 is not quaternion-free and (2) $\Omega_1(P\cap G')\leq Z(P)$ and $N_G(P)$ is 2-nilpotent if and only if $q=3$ and $G\cong GL_2(3)$.

• # Author Affiliations

1. School of Mathematics and Information Science, Yantai University, Yantai 264005, China
2. University of Primorska, IAM, Muzejski trg 2, 6000 Koper, Slovenia

• # Proceedings – Mathematical Sciences

Volume 132, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019