A note on restriction of characters of alternating groups to Sylow subgroups (Q1755556)

The author restricts irreducible characters of alternating groups of degree divisible by \(p\) to their Sylow \(p\)-subgroups and study the number of linear constituents. The main result of the article is the following Theorem A. Let \(n\) be a natural number and let \(p\) be a prime. If \(\chi\in\mathrm{Irr}(A_{n})\) has degree divisible by \(p\), then the restriction \(\chi Q_{n}\) has at least \(p\) different linear constituents.