论文标题
有力的nilpotent组为2或小订单
Powerfully nilpotent groups of rank 2 or small order
论文作者
论文摘要
在本文中，我们继续研究有力的尼尔氏群体。这些是拥有一系列特殊类型的中央系列的功能强大的$ P $组。对于每个这样的组，一个人都可以连接一个强大的尼尔特式类别，该类别自然而然地导致了强大的瓶子和祖先树的分类。在本文中，我们将对有力的nilpotent组进行完整分类，该组排名$ 2 $。然后，该分类将用于达到一个精确的公式，用于有力的nilpotent组$ 2 $和订购$ p^{n} $的数量。我们还将对这些群体的祖先树进行详细分析。然后，该论文的第二部分专门针对有强大的nilpotent订单组的完整分类，最高为$ p^{6} $。
In this paper we continue the study of powerfully nilpotent groups. These are powerful $p$-groups possessing a central series of a special kind. To each such group one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper we will give a full classification of powerfully nilpotent groups of rank $2$. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank $2$ and order $p^{n}$. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to $p^{6}$.
