Young's seminormal form and simple modules for $S_n$ in characteristic $p$

We realize the integral Specht modules for the symmetric group $S_n$ as induced modules from the subalgebra of the group algebra generated by the Jucys-Murphy elements. We deduce from this that the simple modules for $F{S}_n$ are generated by reductions modulo $p$ of the corresponding Jucys-Murphy idempotents.