不存在恰有15个Sylow 7-子群的有限群  

There Exists No Finite Group with Exactly 15 Sylow 7-Subgroups

作　　者：钟凌锋 周伟[1] ZHONG Ling-feng;ZHOU Wei(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2020年第4期9-12,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671324).

摘　　要：运用极小反例来确定群的阶和它的Sylow 7-子群的阶,利用初等方法证明了不存在恰有15个Sylow 7-子群的有限群.In this paper,we use minimal counterexamples to determine the order of the group and its Sylow 7-subgroups,by elementary methods,prove that there exists no finite group with exactly 15 Sylow 7-subgroups.

关 键 词：SYLOW P-子群 SYLOW定理 共轭 

分 类 号：O152.1[理学—数学]