For a finite group G, let ψ(G) denote the sum of element orders of G. If n is a positive integer let Cn be the cyclic group of order n. It is known that ψ(Cn) is the maximum value of ψ on the set of groups of order n, and ψ(G) = ψ(Cn) if and only if G is cyclic of order n. In this paper, we investigate the second largest value of ψ on the set of groups of order n and the structure of groups G of order n with this value of ψ(G) when n is odd.

中文翻译：

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奇数组中元素阶的总和

对于有限群G， 让ψ(G)表示元素阶数的总和G. 如果n是一个正整数Cn是有序的循环群n. 众所周知ψ(Cn)是最大值ψ在有序组的集合上n， 和ψ(G) = ψ(Cn)当且仅当G是有序循环的n. 在本文中，我们研究了ψ在有序组的集合上n和组的结构G有秩序的n与这个值ψ(G)什么时候n很奇怪。