论文标题
关于$ P $ - 组和应用的常规功率结构
On the regular power structure of $p$-groups and applications
论文作者
论文摘要
在本文中，我们给出了限制性伯恩赛德问题的基本证据，以及Hughes猜想有限的$ P $ - 格鲁普斯，并具有霍尔的常规电源结构属性。此外，在这种情况下，我们确定有限$ d $ - 生成器$ p $ - 固定指数的订单的明确约束。提出了具有常规功率结构的$ P $ - 组的进一步应用。例如，我们简短地证明了强大的$ p $ groups重要属性；也就是说，此类$ g $的子组的发电机数量最少是生成$ g $所需的数字。
In this paper, we give elementary proofs of the Restricted Burnside Problem and the Hughes Conjecture for finite $p$-groups with Hall's regular power structure property. Moreover, in this setting we determine an explicit bound on the order of a finite $d$-generator $p$-group of fixed exponent. Further applications of $p$-groups with regular power structure are presented. For example, we give a short new proof of an important property of powerful $p$-groups; namely, that the minimal number of generators of a subgroup of such a group $G$ is at most the number needed to generate $G$.
