We prove that there exists a universal constant D such that if p is a prime divisor of the index of the Fitting subgroup of a finite group G, then the number of conjugacy classes of G is at least $Dp/\log_2p$. We conjecture that we can take $D=1$ and prove that for solvable groups, we can take $D=1/3$.

中文翻译：

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质因数和有限群的共轭类数

我们证明存在一个通用常数D使得如果p< a i=4> 是有限群拟合子群索引的素数G，则 的共轭类数G 至少为 $Dp/\log_2p$。我们猜想我们可以取 $D=1$ 并证明对于可解群，我们可以取 $D =1/3$。