Coprimeness among irreducible character degrees of finite solvable groups

Diane Benjamin
Department of Mathematics, 
University of Wisconsin-Platteville, 
Platteville, 
Wisconsin 53818 

Proc. Amer. Math. Soc. 125 (1997), 2831-2837.

Abstract. Given a finite solvable group $G$, we say that $G$ has property 
$P_k$ if every set of $k$ distinct irreducible character degrees of $G$ is
(setwise) relatively prime. Let $k(G)$ be the smallest positive integer 
such that $G$ satisfies property $P_k$. We derive a bound, which is quadratic
in $k(G)$, for the total number of irreducible character degrees of $G$. 
Three exceptional cases occur; examples are constructed which verify
the sharpness of the bound in each of these special cases.