论文标题
具有最小特征惯性的Abelian P组
Abelian p-groups with minimal characteristic inertia
论文作者
论文摘要
对于Abelian P组，Goldsmith，Salce等人引入了最小的全惯性概念。与此同时，我们定义了最小特征惯性的概念，并探索那些具有最小特征惯性的P-primary Abelian群体。我们确定了一个令人惊讶的结果，即对于每个Abelian P组A，正方形A \ Oplus A具有最小的特征惯性，并且只有当它具有最小的全惯性。我们还获得了这两个属性之间的其他关系。具体而言，我们展示了没有属性的群体，以及我们通过环/模块理论的混凝土复杂结构所展示的，对于任何Prime P，对于任何Prups，都有一个具有最小特征惯性的P组，而这些惯性不具有最小的全惯性。
For Abelian p-groups, Goldsmith, Salce, et al., introduced the notion of minimal full inertia. In parallel to this, we define the concept of minimal characteristic inertia and explore those p-primary Abelian groups having minimal characteristic inertia. We establish the surprising result that, for each Abelian p-group A, the square A \oplus A has the minimal characteristic inertia if, and only if, it has the minimal full inertia. We also obtain some other relationships between these two properties. Specifically, we exhibit groups which do not have neither of the properties, as well as we show via a concrete complicated construction from ring/module theory that, for any prime p, there is a p-group possessing the minimal characteristic inertia which does not possess the minimal full inertia.
