| 阿贝尔群与极大类p-群的半直积的Coleman自同构 |
| |
| 引用本文： | 李正兴,海进科.阿贝尔群与极大类p-群的半直积的Coleman自同构[J].数学物理学报(A辑),2012,32(2):344-348. |
| |
| 作者姓名： | 李正兴 海进科 |
| |
| 作者单位： | 青岛大学数学科学学院 山东青岛 266071 |
| |
| 基金项目： | 国家自然科学基金(11071155, 11171169)和山东省自然科学基金(Y2008A03)资助 |
| |
| 摘 要： | 设G=A\×P是阿贝尔群$A$与极大类p -群P的半直积,其中P中的元以幂自同构的方式作用于A. 该文证明了G的每个Coleman自同构都是内自同构.作为该结果的一个直接推论, 作者得到了这样的群$G$有正规化子性质.
|
| 关 键 词： | 整群环 Coleman自同构 正规化子性质 |
| 收稿时间： | 2010-07-08 |
| 修稿时间： | 2011-12-06 |
Coleman Automorphisms of Semidirect Products of Abelian Groups by p-groups of Maximal Class |
| |
| LI Zheng-Xing,HAI Jin-Ke.Coleman Automorphisms of Semidirect Products of Abelian Groups by p-groups of Maximal Class[J].Acta Mathematica Scientia,2012,32(2):344-348. |
| |
| Authors: | LI Zheng-Xing HAI Jin-Ke |
| |
| Institution: | College of Mathematics, Qingdao University, Shandong Qingdao 266071 |
| |
| Abstract: | Let G=A×P be the semidirect product of an abelian group A and a p-group P of maximal class, where P acts on A by leaving every cyclic subgroup of A invariant. It is shown that every Coleman automorphism of G is an inner automorphism. As an immediate consequence, we obtain that the normalizer property holds for such group G. |
| |
| Keywords: | Integral group ringzz Coleman automorphismzz Normalizer propertyzz |
|
| 点击此处可从《数学物理学报(A辑)》浏览原始摘要信息 |
| 点击此处可从《数学物理学报(A辑)》下载免费的PDF全文 |
