On the number of $p^{\prime }$-degree characters in a finite group

Abstract

Let $p$ be a prime divisor of the order of a finite group $G$. Then $G$ has at least $2\sqrt{p-1}$ complex irreducible characters of degrees prime to $p$. In case $p$ is a prime with $\sqrt{p-1}$ an integer this bound is sharp for infinitely many groups $G$.

References in corpus (1)

• A lower bound for the number of conjugacy classes of a finite group