Blocks of small defect

Let G be a finite solvable group, let p   be a prime such that p≥5p≥5 and Op(G)=1Op(G)=1, and we denote |G|p=pn|G|p=pn, then G   contains a block of defect less than or equal to ⌊3n5⌋. Let G   be a finite solvable group and let papa be the largest power of p   dividing χ(1)χ(1) for an irreducible character χ of G  , we show that |G:F(G)|p≤p3a|G:F(G)|p≤p3a for p≥5p≥5.