A note on 2-nilpotence of finite groups

作者：Shi, Jiangtao; Zhang, Cui^*

来源：Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2013, 123(2): 235-238.

DOI：10.1007/s12044-013-0122-y

• Finite group
• 2-nilpotent group
• quaternion-free

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 boolean AND G') <= 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 boolean AND G') <= Z(P) and N-G(P) is 2-nilpotent if and only if q = 3 and G congruent to GL(2)(3).

• 出版日期2013-5
• 单位烟台大学