Under the degree of some finite linear groups. II

Abstract:

Let $G$ be a finite group with a cyclic Sylow $p$-subgroup for some prime $p \geq 13$. Assume that $G$ is not of type ${L_2}(p)$, and that $G$ has a faithful indecomposable modular representation of degree $d \leq p$. Some known lower bounds for $d$ are improved, in case the center of the group is trivial, as a consequence of results on the degrees $\pmod p$ of irreducible Brauer characters in the principal $p$-block.