An Arithmetical Condition on the Sizes of Conjugacy Classes of a Finite Group  

作　　者：Yongcai Ren 

机构地区：[1]School of Mathematics,Sichuan University,Chengdu 610064,China

出　　处：《Algebra Colloquium》2022年第3期375-384,共10页代数集刊（英文版）

摘　　要：An element x of a finite group G is said to be primary if the order of x is a prime power.We define csp2(G)as follows:if|x^(G)|is a prime power for every primary element x of G,where x^(G) is the conjugacy class of x in G,then csp2(G)=0;if there exists a primary element x in G such that|x^(G)|is divisible by at least two distinct primes,then csp2(G)=max{|x^(G)||x∈Gis primary,|x^(G)|is divisible by at least two distinct primes}.In this paper we discuss the influence of the number csp2(G)on the structure of G.

关 键 词：finite group primary element conjugacy class size SOLVABLE 

分 类 号：O152.1[理学—数学]