| 陈重穆.关于几乎可解群[J].数学研究及应用,1993,13(4):579~581 |
| 关于几乎可解群 |
| On Almost Solvable Groups |
| 投稿时间：1991-06-20 |
| DOI：10.3770/j.issn:1000-341X.1993.04.020 |
| 中文关键词: |
| 英文关键词: |
| 基金项目: |
|
| 摘要点击次数: 1888 |
| 全文下载次数: 1216 |
| 中文摘要: |
| 本文推广了关于局部有限群的Asar定理及p.Hall—Kulatilaka,Kargapolov定理. |
| 英文摘要: |
| Group G is called almost solvable, if G has a finite normal series such that each factor group of the series is abelian or finite. We show that(1) If locally almost solvable period group G has a finite Sylow p-subgroup, then all Sylow p-subgroups of G are finite and conjuate.(2) Every infinite locally almost solvable group has an infinite abelian subgroup.(3) Suppose that the Sylow p-subgroups of G are locally finite and every finitely generated subgroup of G possesses the "Sylow finite p- property". That is, each finite p-subgroup is isomorphic to some subgroup of each Sylow p-subgroup. If each countable subgroup of G has only countably many Sylow p-subgroups, then all the Sylow p-subgroups of G are conjugate. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
|
|
|
