被至少两个不同素数整除的共轭类长

Conjugacy-Class-Lengths Are Divisible by at Least Two Distinct Prime Numbers

设G是有限群.如果G至少有一个共轭类C的长C被两个不同的素数整除,则定义ccl2(G)=max{C C是G的共轭类,且C被至少两个不同的素数整除};如果G的各共轭类的长是素数的幂,则规定ccl2(G)=0.讨论当ccl2(G)≠0时,ccl2(G)给定的上界对有限非可解群G结构的影响.

Let G be a finite group. If G has at least one conjugacy class C such that ｜C｜ is divisible by at least two distinct primes, then we define ccl2（G）=max{｜C｜｜C is a conjugaey class of G such that ｜C｜ is divisible by at least two distinct primes}. The purpose of this paper is to discuss the influence of a given upper bound of ccl2（G） on the structure of a non-solvable group G when ccl2（G）≠0.