最高阶元素个数为76p的有限群

Finite Groups with 76p Elements of Maximal Order

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。

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.