论文标题
对有限组的元素顺序的总和的概括
A generalization of a result on the sum of element orders of a finite group
论文作者
论文摘要
令$ g $为有限的组，让$ψ（g）$表示$ g $的元素订单之和。众所周知，在$ n $的组集组中，$ n $是一个正整数的最大值$φ$将发生在循环组$ c_n $上。对于Nilpotent群体，我们证明了该结果的自然概括，通过用$ g $的元素订单与元素订单相对于某个$ g $的元素订单而获得。
Let $G$ be a finite group and let $ψ(G)$ denote the sum of element orders of $G$. It is well-known that the maximum value of $φ$ on the set of groups of order $n$, where $n$ is a positive integer, will occur at the cyclic group $C_n$. For nilpotent groups, we prove a natural generalization of this result, obtained by replacing the element orders of $G$ with the element orders relative to a certain subgroup $H$ of $G$.
