| 摘要: |
| 有限群G的一个弱n-Engle条件是指:对于G的2个元素x,y和某个非负整数n,[x,ny]∈Z(G)成立,如果存在G的一个子群K满足HK=G和H∩K≤CoreG(H),则G的一个子群H称为c-可补的.利用极小子群的弱n-Engle条件和4阶循环子群的c-可补性,讨论了G的p-幂零性. |
| 关键词: 有限群 Engle条件 p-幂零群 c-可补子群 |
| DOI： |
| 投稿时间：2003-09-08修订日期：2003-11-03 |
| 基金项目:Supported by Natural Science Foundation of China (10161001) and Natural Science Foundation of Guangxi Normal University. |
|
| A Weak n-Engel Condition and the p-nilpotency of Finite Groups |
|
Zhong Xianggui
|
| (Dept. of Math., Guangxi Normal Univ., 3 Yucailu, Guilin, Guangxi, 541004, China) |
| Abstract: |
| Let G be a finite group.For a weak n-Engel condition of G, we mean that[x,ny]∈Z(G) for two elements x and y of G,where n is a positive integer.A subgroup H of G is called c-supplemented in G if there exists a subgroup K of G such that HK=G and H∩K ≤ CoreG(H).In this paper,we discuss the sufficient conditions of a p-nilpotent group by using supplementation of the cyclic subgroups of order 4 under some assumptions weaker than the n-Engel condition on minimal subgroups of G. |
| Key words: finite group Engel condition p-nilpotent group c-supplemented subgroup |
