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首页> 外文期刊>Journal of algebra and its applications >A classification of exceptional components in group algebras over abelian number fields
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A classification of exceptional components in group algebras over abelian number fields

机译：阿贝尔数域上群代数中特殊成分的分类

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When considering the unit group of OFG (OF the ring of integers of an abelian number field F and a finite group G) certain components in the Wedderburn decomposition of FG cause problems for known generic constructions of units; these components are called exceptional. Exceptional components are divided into two types: type 1 is division rings, type 2 is 2 x 2-matrix rings. For exceptional components of type 1 we provide infinite classes of division rings by describing the seven cases of minimal groups (with respect to quotients) having those division rings in their Wedderburn decomposition over F. We also classify the exceptional components of type 2 appearing in group algebras of a finite group over number fields F by describing all 58 finite groups G having a faithful exceptional Wedderburn component of this type in FG.
机译：当考虑OFG的单位组（阿贝尔数域F和有限群G的整数环）时，FG的Wedderburn分解中的某些分量会导致已知单位通用构造的问题。这些组件称为例外。特殊的组件分为两种类型：类型1是分隔环，类型2是2 x 2矩阵环。对于类型1的特殊分量，我们通过描述在F上的Wedderburn分解中具有那些分隔环的最小组的7种情况（关于商）来提供无限类的分隔环。我们还对出现在组中的类型2的特殊分量进行分类通过描述在FG中具有忠实的此类Wedderburn分量的所有58个有限群G来确定数量域F上有限群的代数。

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