摘要
设G为有限群,C(G)为G的循环子群的集合.|C(G)|对G的结构有一定的影响.例如,G为初等交换2-群当且仅当|C(G)|=|G|.一些作者已经分类了满足|G|-|C(G)|≤3的群.利用循环子群个数与|G|的等式关系,分类了所有满足|G|-|C(G)|=4的有限群.
Let G be a finite group, C(G) is the set of cyclic subgroup of G.| C(G)| has a certain effect on the structure of G. It is well-know that G is a elementary abelian subgroups if and only if | C(G)|=|G| and several authors have investigated groups with |G|-|C(G)|≤3. It is reasonable to describe the finite groups G having |G|-4 cyclic subgroups by using the equality relation of the number of cyclic subgroups.
作者
姜富铭
周伟
JIANG Fu-ming;ZHOU Wei(School of Mathematics and Statistic, Southwest University, Chongqing 400715, China)
出处
《西南师范大学学报（自然科学版）》
CAS
北大核心
2019年第2期14-17,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)
关键词
有限群
2-群
循环子群
finite groups
2-groups
cyclic subgroups
