I want to show that the class of $p$-supersolvable groups is a saturated formation.
I only have the definition of $p$-supersolvable. What do I do?
A group is $p$-supersolvable iff every chief factor either has order $p$ or order coprime to $p$. A chief factor of $G$ is a quotient $H/K$ where (a) $H,K \unlhd G$, (b) $H < K$, and (c) if $H \leq L < K$ and $L \unlhd G$, then $H=L$.
A class $\mathcal{F}$ of groups is a saturated formation if
1) if $G \in \mathcal{F}$ and $H \lhd G$ then $G/H \in \mathcal{F}$.
2) if $G/M, G/N \in \mathcal{F}$ for $M,N \lhd G$, then $G/M\cap N \in \mathcal{F}$.
3) if $G/\phi(G) \in \mathcal{F}$ then $G\in \mathcal{F}$.