最高阶元素个数为4p^2的有限群是可解群

Finite Groups with |M(G)|=4p^2 Elements of Maximal Order Are Solvable

研究了最高阶元素个数对有限群结构的影响.运用群阶的素因子,k阶循环子群共轭类的长,以及K3-单群和K4-单群的有关结论,证明了最高阶元素个数为|M(G)|=4p2的有限群G是可解群,其中p是素数.

Affection on the structure of finite group as the number of maximal order elements is discussed. It is proved that such finite groups with 4p2 maximal order elements are solvable by making use of corresponding results on K3-simple groups and K4-simple groups, as well as the prime factor of the order of a finite group and the length of the conjugate class of cyclic subgroups with order k, where p is a prime