Let $G \leq S_n$ be a permutation group. Also let $G^{(i)}, 1 \leq i \leq n$ be the subgroups of permutation whic fix elements $1,2,\cdots i$. Then $G= G^{(0)} = (G^{(0)}/G^{(1)}) (G^{(1)}/G^{(2)}) \cdots (G^{(n-1)}/G^{(n)})$ (product of quotients) I am trying to understand the matter at page 37 of $\href{http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4567802&tag=1}{this}$ paper. How do we prove this.
