论文标题
关于由算法和几何元素的几何表示的有限基团的结构
On the structure of finite groups determined by the arithmetic and geometric means of element orders
论文作者
论文摘要
在本文中，我们考虑了有限群体的元素顺序算术和几何方法有关的两个函数，表明此类功能的某些下限强烈影响组结构。特别是，对于每个Prime $ p $，我们证明有限组为$ p $ nilpotent，即，一个元素的元素为$ p'$ - 订单形成一个普通子组。此外，我们表征了有限的循环基团，这些循环群具有规定的主要除数。
In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions strongly affect the group structure. In particular, for every prime $p$, we prove a sufficient condition for a finite group to be $p$-nilpotent, that is, a group whose elements of $p'$-order form a normal subgroup. Moreover, we characterize finite cyclic groups with prescribed number of prime divisors.
