Let $p$ be a prime such that $p \geq 5$. Let $G$ be a finite $p$-solvable group and let $p^a$ be the largest power of $p$ dividing $\chi(1)$ for an irreducible character $\chi$ of $G$, we show that $|G:F(G)|_p \leq p^{ 5.5a}$. Let $G$ be a finite $p$-solvable group with trivial maximal normal solvable subgroup and we denote $|G|_p=p^n$, then $G$ contains a block of defect less than or equal to $\lfloor \frac { 2n} { 3} \rfloor$.
Categories: math.GR