\(\mathcal{P}\)-characters of \(\mathrm{PSL}(2,q)\) (Q6101416)

Let \(H\) be a subgroup of a group \(G\), the transitive permutation character \((1_{H})^{G}\) is said to be multiplicity-free if all of its irreducible constituents are distinct. A \(\mathcal{P}\)-character of \(G\) is an irreducible character, which is a constituent of the permutation character \((1_{M})^{G}\) for some maximal subgroup \(M\) of \(G\). In the paper under review, the authors determine the \(\mathcal{P}\)-characters of \(P=\mathrm{PSL}(2, q)\) and check which of the permutation characters \((1_{M})^{P}\) are multiplicity-free.