论文标题
一些不可还原性格度的平均值
The Average of Some Irreducible Character Degrees
论文作者
论文摘要
我们有兴趣确定不可约字符的平均值的界限，该学位不可用某些主要$ p $排除，该$ p $保证有限的of od odd odd odd订单为$ p $ nilpotent。我们发现一个取决于Prime $ p $的界限。如果我们通过修复复数的子字段$ k $进一步限制平均值，然后计算出不可减至的字符的平均值的平均值，该字符的度量不可简化$ p $，并且在$ k $中具有值，那么我们将看到我们获得的界限取决于$ p $和$ k $。此外，我们找到了使这些界限最大的示例。
We are interested in determining the bound of the average of the degrees of the irreducible characters whose degrees are not divisible by some prime $p$ that guarantees a finite group $G$ of odd order is $p$-nilpotent. We find a bound that depends on the prime $p$. If we further restrict our average by fixing a subfield $k$ of the complex numbers and then compute the average of the degrees of the irreducible characters whose degrees are not divisible by $p$ and have values in $k$, then we will see that we obtain a bound that depends on both $p$ and $k$. Moreover, we find examples that make those bounds best possible.
