有限群正规子群的算法及S_7子群的正规子群

Algorithm of normal subgroup of finite group and S7 subgroup's normal subgroup

在群的正规闭包理论的基础上,定义了有限群的正规闭包链表,证明了一个有限群G的正规闭包链表恰好包含了G的所有正规子群,从而获得了求有限群所有正规子群的方法,以及求置换群的所有正规子群的算法,且依此算法计算得S7的子群的所有正规子群.

Based on the group＇s theory of formal closure, this article has a definition for formal closure list of finite groups and proves that a formal closure list of finite group G just contains all normal subgroups of G. And we acquired the method of finding all normal subgroups of finite groups and the algorithm of finding all normal subgroups of permutation group. According to that, processes of calculating all normal subgroups of S7 ＇subgroups are designed.