A note on 2-nilpotence of finite groups

被引：0
|
作者：
JIANGTAO SHI
CUI ZHANG
机构：
[1] Yantai University,School of Mathematics and Information Science
[2] University of Primorska,undefined
[3] IAM,undefined
来源：
Proceedings - Mathematical Sciences | 2013年 / 123卷
关键词：
Finite group; 2-nilpotent group; quaternion-free;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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) Ω1(P ∩  G′) ≤ Z(P) and NG(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) Ω1(P ∩ G′) ≤ Z(P) and NG(P) is 2-nilpotent if and only if q = 3 and G ≅ GL2(3).
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页码：235 / 238
页数：3
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