Remark 2

Let $a$ and $b$ be vertices of G. The mapping of $G_{a,b}$ into $(G/H)_{p(a),p(b)}$ deduced from $p$ is surjective. Let in fact $u$ be an arrow of $G/H$ joining $p(a)$ to $p(b)$; it is the class modulo $\mathscr{R}$ of an arrow $f$ of G. The origin $o(f)$ of $f$ belongs to the orbit of $a$ in H; hence there exists an arrow $x$ in H joining $a$ to $o(f)$. Analogously, there exists an arrow $y$ in H joining $t(f)$ to $b$. Then $f'=xf y$ is an element of $G_{a,b}$ whose class modulo $\mathscr{R}$ is $u$.