Under the degree of some finite linear groups. II

Abstract

Let G G be a finite group with a cyclic Sylow p p -subgroup for some prime p ≥ 13 p \geq 13 . Assume that G G is not of type L 2 ( p ) {L_2}(p) , and that G G has a faithful indecomposable modular representation of degree d ≤ p d \leq p . Some known lower bounds for d d are improved, in case the center of the group is trivial, as a consequence of results on the degrees ( mod p ) \pmod p of irreducible Brauer characters in the principal p p -block.