对称群S_(4)中的S-拟正规嵌入子群和几乎SS-嵌入子群研究  

Study of S-quasinormally Embedded Subgroups and Nearly SS-embedded Subgroups in the Symmetry Group S_(4)

作　　者：张佳 朱丽羽 黄潇 ZHANG Jia;ZHU Li-yu;HUANG Xiao(School of Mathematics and Information,China West Normal University,Nanchong,Sichuan,637009)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《贵州师范学院学报》2024年第6期1-5,共5页Journal of Guizhou Education University

基　　金：国家自然科学基金项目“关于Monakhov问题和Flavell问题及其在特征标中应用的一些研究”(12001436);四川省自然科学基金项目“密码学和量子计算中两个群论问题的研究”(2022NSFSC1843);教育部春晖计划合作科研项目“有限群中相关信息安全的Bertram问题”(HZKY20220567)。

摘　　要：为探讨四次对称群S_(4)的所有S-拟正规子群、S-拟正规嵌入子群和几乎SS-嵌入子群,结合置换的计算方法,利用其定义和相关引理得出了相应的结果。结果显示:S_(4)的S-拟正规子群为N_(1),K_(4),A_(4),S_(4);S_(4)的S-拟正规嵌入子群有N_(1),N_(11),N_(12),N_(13),N_(14),K_(4),N_(26),N_(27),N_(28),A_(4),S_(4);S_(4)的几乎SS-嵌入子群有N_(1),N_(2),N_(3),N_(4),N_(5),N_(6),N_(7),N_(11),N_(12),N_(13),N_(14),K_(4),N_(22),N_(23),N_(24),N_(25),N_(26),N_(27),N_(28),A_(4),S_(4)。In order to investigate all S-quasinormal subgroups,S-quasinormally embedded subgroups and nearly SS-embedded subgroups of the quartic symmetry group S_(4),the corresponding results are obtained by using the definition and correlation lemma,combined with the calculation method of permutation.The results show that the S-quasinormal subgroups of S_(4)are N_(1),K_(4),A_(4),S_(4);the S-quasinormally embedded subgroups of S_(4)are N_(1),N_(11),N_(12),N_(1)3,N_(1)4,K_(4),N_(26),N_(27),N_(28),A_(4),S_(4);the nearly SS-embedded subgroups of S_(4)are N_(1),N_(2),N_(3),N_(4),N_(5),N_(6),N_(7),N_(11),N_(12),N_(13),N_(14),K_(4),N_(22),N_(23),N_(24),N_(25),N_(26),N_(27),N_(28),A_(4),S_(4)

关 键 词：S_(4) S-拟正规 S-拟正规嵌入 几乎SS-嵌入 

分 类 号：O152.1[理学—数学]