| 摘要: |
| 证明有限群G是幂零的,如果满足:G'幂零,G有素数r阶自同构α使得r∉π(CG(α)),并且G有α-不变的幂零极大子群H使得CG(α)≤ Φ(H)且H的Sylow2-子群的幂零类 ≤ 2.该结果推广了Thompson定理. |
| 关键词: 有限群 自同构 极大子群 幂零群 |
| DOI： |
| 投稿时间：2007-03-28修订日期：2007-06-14 |
| 基金项目:广西科学基金项目(0575050,0640061);广西研究生教育创新计(2007106020701M51)资助 |
|
| A Note on Thompson Theorem |
|
ZHONG Xiang-gui, LI Yong-gang
|
| (School of Mathematical Sciences, Guangxi Normal University, Guilin, Guangxi, 541004, China) |
| Abstract: |
| It is proved that a finite group G is nilpotent if G' is nilpotent and G has prime r order automorphism α such that r∉π (CG (α)) for α-invarant nilpotent maximal subgroup H of G with CG (α) ≤ Φ (H) and c (H2) ≤ 2.This conclusion generalizing the theorem of Thompson. |
| Key words: finite group automorphism maximal subgroup nilpotent group |
