Theorem 9.3.1 in Hall's group theory says: Let $G$ be a solvable group and $|G|=m\cdot n$, where $% m=p_{1}^{\alpha _{1}}\cdot \cdot \cdot p_{r}^{\alpha _{r}}$, $(m,n)=1$. Let $% \pi =\{p_{1},...,p_{r}\}$ and $h_{m}$ be the number of $\pi -$Hall subgroups of $G$. Then $h_{m}=q_{1}^{\beta _{1}}\cdot \cdot \cdot q_{s}^{\beta _{s}}$ satisfies the following condition for all $i\in \{1,2,...,s\}$.

$% q_{i}^{\beta _{i}}\equiv 1$ (mod $p_{j}$), for some $p_{j}$.

This question arises now that if we replace assumption solvable group with $p$-solvable group whether again Theorem is true. In the other words: Is it true the following claim? Or is there any counterexample for the claim?

Let $G$ be a $p$-solvable group and $|G|=p^{\alpha }\cdot n$ such that $(p^{\alpha },n)=1$($p\neq 2$). Let $% h_{m}$ be the number of Sylow $p-$subgroups of $G$. Then $h_{m}=q_{1}^{\beta _{1}}\cdot \cdot \cdot q_{s}^{\beta _{s}}$ satisfies the following condition for all $i\in \{1,2,...,s\}$.

$q_{i}^{\beta _{i}}\equiv 1$ (mod $p$).