THE AVERAGE OF SOME IRREDUCIBLE CHARACTER DEGREES

Source abstract

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. There was found to be a bound which depends on the prime $p$. By further restricting the average by fixing a subfield $k$ of the complex numbers and then computing the average of the degrees of the irreducible characters whose degrees are not divisible by $p$ and have values in $k$, then a bound was obtained which depends on both $p$ and $k$. Examples are provided which show best possible bounds.