摘要
通过模仿非幂零二维李代数L_(0)∶[x,y]=x,构造出一个有限群族{N_(n,q,b)},弄清楚这些群的基本构造,并证明了对于任意的d,当n(q-1)^(d)时,有限群G是非幂零的当且仅当G含有{N_(n,q,b)}中一个非幂零成员作为子群.
By imitating the two-dimensional Lie algebra L_(0):[x,y]=x which is not nilpotent,we introduce a class of finite groups N_(n,q,b).We determine properties of these groups,and prove that a finite group G isn’t nilpotent if and only if G contains a member of {N_(n,q,b)} which is not nilpotent as a subgroup,when n(q-1)^(d) for any d.
作者
吴晓彤
陈智
WU Xiaotong;CHEN Zhi(School of Mathematics,Hefei University of Technology,Hefei 230601,China)
出处
《大学数学》
2022年第5期23-26,共4页
College Mathematics
关键词
有限群
幂零群
李代数
finite group
nilpotent group
Lie algebra
