论文标题
有限群的可溶性按元素订单的权力之和
The solvability of a finite group by the sum of powers of element orders
论文作者
论文摘要
我们证明了有限组的解决性的新标准，具体取决于功能$ψ_K（g）$，该功能定义为$ g $的元素订单的$ k $ th powers。我们表明，我们的结果可用于显示某些组的解决性，而这些组的可溶性并不从较早的类似结果中遵循，我们强调以下内容：查看$ψ_k（g）$ for $ k> 1 $ $> 1 $对于获取有关$ g $组的更多信息是有用的。
We prove a new criterion for the solvability of the finite groups, depending on the function $ψ_k(G)$ which is defined as the sum of $k$-th powers of the element orders of $G$. We show that our result can be used to show the solvability of some groups for which the solvability does not follow from earlier similar kind of results and we emphasize the following: looking at $ψ_k(G)$ for $k>1$ can be useful to get further pieces of information about the group $G$.
