| 具有阿贝尔Sylow 2-子群的有限群的整群环的正规化子性质 |
| |
| 引用本文： | 海进科,李正兴.具有阿贝尔Sylow 2-子群的有限群的整群环的正规化子性质[J].数学学报,2012(1):187-192. |
| |
| 作者姓名： | 海进科 李正兴 |
| |
| 作者单位： | 青岛大学数学科学学院 |
| |
| 基金项目： | 国家自然科学基金资助项目(11171169,11071155);山东省自然科学基金资助项目(Y2008A03) |
| |
| 摘 要： | Mazur猜想:具有阿贝尔Sylow 2-子群的有限群有正规化子性质.设G是一个有限群,N是G的一个正规子群且Z(G/N)仅有平凡单位,本文建立了由Z(G/N)中单位诱导的G的自同构与N的Coleman自同构之间的联系,在此基础上证明了若G是一个具有阿贝尔Sylow 2-子群的有限群且Z(G/F*(G))仅有平凡单位,则Mazur猜想对G成立.
|
| 关 键 词： | 正规化子性质 平凡单位 Coleman自同构 |
The Normalizer Property for Integral Group Rings of Finite Groups with Abelian Sylow 2-Subgroups |
| |
| Jin Ke HAI Zheng Xing LI.The Normalizer Property for Integral Group Rings of Finite Groups with Abelian Sylow 2-Subgroups[J].Acta Mathematica Sinica,2012(1):187-192. |
| |
| Authors: | Jin Ke HAI Zheng Xing LI |
| |
| Institution: | Jin Ke HAI Zheng Xing LI College of Mathematics,Qingdao University,Qingdao 266071,P.R.China |
| |
| Abstract: | Mazur conjectured that the normalizer property holds for finite groups with abelian Sylow 2-subgroups.Let G be a finite group and let N be a normal subgroup of G such that Z(G/N) has only trivial units.In this paper,a connection is established between the automorphisms of G induced by units in Z(G/N) and Coleman automorphisms of N.Based on this connection,we confirm that if G is a finite group with abelian Sylow 2-subgroups and Z(G/F~*(G)) has only trivial units then Mazur’s conjecture holds for G. |
| |
| Keywords: | the normalizer property trivial unit Coleman automorphism |
| 本文献已被 CNKI 等数据库收录！ |
