中文摘要：

设G为有限群，l是一个正整数，｜Ml（G）｜是G的l阶元素的集合，k表示G中元素的最高阶。特别地｜M（G）｜=｜Mk（G）｜。讨论了群的最高阶元素个数为｜M（G）｜=76p的有限群，得到了如下定理：设G是最高阶元素个数为76p的有限群，其中素数p〉5，则G可解。

英文摘要：

Let G be a finite group, l is a positive and ｜Ml（G）｜ denotes the set of elements of order l. k is the largest order of elements of G. Especially ｜M（G）｜ = ｜Mk（G）｜ The finte groups with 76p elements of maximal order were discussed, and a theorem was gotten as follows： Suppose G is a finite group with ｜M（G）｜ = 76p elements of maximal order, where p is a prime and p 〉 5, then G is solvable.