论文标题
p频繁的共轭类和p理性的不可减少字符
p-Regular conjugacy classes and p-rational irreducible characters
论文作者
论文摘要
让$ g $是一组有限的订单组，可除以$ p $。 $ p $ - regular和$ p'$的数量 - $ g $的常规共轭类别至少为$ 2 \ sqrt {p-1} $。同样，$ p $ - 理性的数量和$ p'$ - $ g $的有理不可约的字符至少为$ 2 \ sqrt {p-1} $。在此过程中，我们证明了在有限的简单谎言类型组中的$ p $等级类数的统一下限，该类别的等级和大小的基础字段的数量。
Let $G$ be a finite group of order divisible by a prime $p$. The number of $p$-regular and $p'$-regular conjugacy classes of $G$ is at least $2\sqrt{p-1}$. Also, the number of $p$-rational and $p'$-rational irreducible characters of $G$ is at least $2\sqrt{p-1}$. Along the way we prove a uniform lower bound for the number of $p$-regular classes in a finite simple group of Lie type in terms of its rank and size of the underlying field.
