Representations of the symmetric group are reducible over simply transitive subgroups (Q1586860)

The following result is proved. Main Theorem: Let \(F\) be a field of characteristic \(p>2\), \(n\geq 4\), \(G\leq S_n\), where \(S_n\) is the symmetric group of degree \(n\), and let \(D\) be a simple \(FS_n\)-module with \(\dim(D)>1\). If the restriction \(D_G\) is irreducible then either \(G\leq S_{n-1}\) of \(G\) is 2-transitive.