不可解群的共轭类数与幂零子群  

Conjugacy Class Numbers of Nonsolvable Groups and Nilpotent Subgroups

作　　者：董淑琴 DONG Shuqin(School of Mathematics and Statistics,Huaiyin Normal University,Huai'an 223300,China)

机构地区：[1]淮阴师范学院数学与统计学院,江苏淮安223300

出　　处：《淮阴师范学院学报(自然科学版)》2025年第1期19-21,51,共4页Journal of Huaiyin Teachers College(Natural Science Edition)

基　　金：国家自然科学基金项目(12201236)。

摘　　要：设有限群G不可解,且其截段中不含L_(2)(5)和L_(2)(7).利用有限单群分类定理,得到:若B为G的幂零子群,则有3|BO_(π)(G)/O_(π)(G)|<|G|/k(G).这里k(G)为G的共轭类数,π=π(B)为|B|的素因子集合.在共轭类数与不可解群的幂零子群阶之间的数量关系上,所得结论改进了相关研究的结果.Let G be a nonsolvable group with no sections isomorphic to L_(2)(5)and L_(2)(7).Using the classification of finite simple groups,the result is obtained:if B is a nilpotent subgroup of G,then 3|BO_(π)(G)/O_(π)(G)|<|G|/k(G),where k(G)is the number of conjugacy classes of G,and π=π(B)is the set of prime divisors of|B|.The conclusion obtained in this paper improves the relevant results on the quantitative relationship between the conjugacy class numbers and the order of nilpotent subgroups of nonsolvable groups.

关 键 词：共轭类数 幂零子群 SYLOW子群 不可解 有限单群 

分 类 号：O152.1[理学—数学]