Representations of the alternating group which are irreducible over subgroups (Q2766445)

Let \(F\) be an algebraically closed field of charateristic \(p\geq 0\) and let \(A_n\) denote the alternating group of degree \(n\). The authors of the paper under review are interested in finding the pairs \((G,E)\) where \(E\) is an irreducible \(FA_n\)-module and \(G\) is a proper subgroup of \(A_n\) such that the restriction of \(E\) to \(G\) is irreducible. They give a list of such pairs for \(p>3\) and \(n\geq 5\). The case \(p=0\) was treated by \textit{J. Saxl} [J. Algebra 111, 210-219 (1987; Zbl 0633.20008)]. Therefore the problem for the cases \(p=2\) and 3 is open.