论文标题
整体群环中的nilpotent分解
Nilpotent Decomposition in Integral Group Rings
论文作者
论文摘要
据说有限的组$ g $具有nilpotent分解属性（ND），如果每个nilpotent元素$α$的整体组环$ \ mathbb {z} [g] $一个人都有$αe$也属于每个prilitive central Idempotent Idempotent $ e e e $ e e $ e a $ \ mathbb {q} [g] $。 Hales，Passi和Wilson，Liu and Passman的结果表明，该特性是对整体群环的乘法Jordan分解的研究至关重要的。如果$ g $及其所有子组都拥有ND，那么Liu和Passman表明，$ G $具有属性SSN，也就是说，对于子组$ h $，$ y $和$ g $的$ h $和$ n $ g $，如果$ n \ lhd h $ and $ y \ y \ y \ subseteq h $ then $ n \ subseteq y $或$ yn $ yn $ h $ in $ h $ in $ h $ in in in in $ h $ in in in in in in in in in in in in in in in in in in in in in in in in in in in in。并已经描述了这样的群体。在本文中，我们研究了整体式戒指中的nilpotent分解属性，并对有限的SSN组$ g $进行了分类，以使理性组代数$ \ mathbb {q} [g} [g] $只有一个wedderburn组件，而不是分区环。
A finite group $G$ is said to have the nilpotent decomposition property (ND) if for every nilpotent element $α$ of the integral group ring $\mathbb{Z}[G]$ one has that $αe$ also belong to $\mathbb{Z}[G]$, for every primitive central idempotent $e$ of the rational group algebra $\mathbb{Q}[G]$. Results of Hales, Passi and Wilson, Liu and Passman show that this property is fundamental in the investigations of the multiplicative Jordan decomposition of integral group rings. If $G$ and all its subgroups have ND then Liu and Passman showed that $G$ has property SSN, that is, for subgroups $H$, $Y$ and $N$ of $G$, if $N\lhd H $ and $Y\subseteq H$ then $N\subseteq Y$ or $YN$ is normal in $H$; and such groups have been described. In this article, we study the nilpotent decomposition property in integral group rings and we classify finite SSN groups $G$ such that the rational group algebra $\mathbb{Q}[G]$ has only one Wedderburn component which is not a division ring.
