On the Normal Subgroup with Coprime 𝐺-Conjugacy Class Sizes

Proceedings Mathematical Sciences

Guiyun Chen³  Xianhe Zhao¹  Jiaoyun Shi² 

[1] School of Mathematics and Statistics, Southwest University, Chongqing 00, People’s Republic of China$$;School of Mathematical Science, Fudan University, Shanghai 00, People’s Republic of China$$;College of Mathematics and Information Science, Henan Normal University, Xinxiang Henan 00, People’s Republic of China$$

关键词: Finite group;    normal subgroup;    𝐺-conjugacy class size;    Frobenius group.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝑁 be a normal subgroup of a group 𝐺. The positive integers 𝑚 and 𝑛 are the two longest sizes of the non-central 𝐺-conjugacy classes of 𝑁 with 𝑚>𝑛 and (𝑚,𝑛)=1. In this paper, the structure of 𝑁 is determined when 𝑛 divides $|N/Ncap Z(G)|$. Some known results are generalized.

【 授权许可】

Unknown