The solvable degree of a Schur algebra

Abstract

The solvable degree of a Schur algebra $D$ is the greatest common divisor of all integers $n$ such that $D^{n\times n}$ is a direct summand of the rational group algebra $\Q G$ for some finite solvable group $G$. The main result of this paper gives divisibility conditions on the solvable degree depending on the center and the rational primes that divide the discriminant of $D$.