论文标题
根据有限组的平均顺序
On the average order of a finite group
论文作者
论文摘要
令$ o（g）$为有限的$ g $的平均订单。我们表明，如果$ o（g）<c $，其中$ c \ in \ lbrace \ frac {13} {6} {6}，\ frac {11} {4} {4} \ rbrace $，则$ g $分别是基本的Abelian 2组或一个可求解的组。另外，我们证明包含所有有限组的平均订单的集合在$ [a，\ infty）$中均不密度，对于[0，\ frac {13} {6}] $，所有$ a \ in $ [a，\ infty）$。我们还概述了与平均顺序的整数值有关的一些结果。由于小组元素订单是一个受欢迎的研究主题，因此我们对整个论文中有限组的平均顺序提出了一些开放问题。
Let $o(G)$ be the average order of a finite group $G$. We show that if $o(G)<c$, where $c\in \lbrace \frac{13}{6}, \frac{11}{4}\rbrace$, then $G$ is an elementary abelian 2-group or a solvable group, respectively. Also, we prove that the set containing the average orders of all finite groups is not dense in $[a, \infty)$, for all $a\in [0, \frac{13}{6}]$. We also outline some results related to the integer values of the average order. Since group element orders is a popular research topic, we pose some open problems concerning the average order of a finite group throughout the paper.
