摘要
对任意两个不同阶元素可交换的p-群进行了研究,得到:(1)当G为方次数为p的p-群时,G中任意两个不同阶元素均可交换;当G为方次数大于p的p-群时,G中任意两个不同阶元素均可交换充分必要条件是Ωe-1(G)≤Z(G)。(2)设G为非交换的p-群,若G中任意两个非正规的子群均有相同的阶,则G中任意两个不同阶元素均可交换。
p-groups G such that every two elements of G of distict orders are permutable are inverstigated, and obtained the following two results： （1） when G exponent p, then every two elements of G of distict orders are permutable, when G exponent greater than p ,then all every two elements of G of distict orders be permutable if only if Ωe-1（G）≤Z（G）. （2） Let G be nonabelian p -groups, if all nonnormal subgroups have the same order , then every two elemnts of G of distict orders are permutable.
出处
《咸阳师范学院学报》
2015年第6期49-50,共2页
Journal of Xianyang Normal University
基金
咸阳师范学院科研基金项目(10XSYK203)
