论文标题
组环的结构和整体圈环的组组：邀请
Structure of group rings and the group of units of integral group rings: an invitation
论文作者
论文摘要
在过去的三十年中，在构建单位组$ \ u（\ z g）$ $ \ z g $的单位组$ \ u（\ z g）$的大型无扭转子组（即有限指数的子组）方面取得了基本进展。这些结构依赖于$ \ z g $中单位的明确结构，主要结果的证明利用了理性群体代数$ \ q g $的Wedderburn组件的描述。后者依赖于原始中央基金会的明确结构以及$ g $的合理表示。事实证明，减少两个度表示的存在起着至关重要的作用。尽管单位组远非被理解，但已经获得了该组的某些结构结果。在本文中，我们对一些基本结果和必需技术进行了调查。
During the past three decades fundamental progress has been made on constructing large torsion-free subgroups (i.e. subgroups of finite index) of the unit group $\U (\Z G)$ of the integral group ring $\Z G$ of a finite group $G$. These constructions rely on explicit constructions of units in $\Z G$ and proofs of main results make use of the description of the Wedderburn components of the rational group algebra $\Q G$. The latter relies on explicit constructions of primitive central idempotents and the rational representations of $G$. It turns out that the existence of reduced two degree representations play a crucial role. Although the unit group is far from being understood, some structure results on this group have been obtained. In this paper we give a survey of some of the fundamental results and the essential needed techniques.
