Linear characters of Sylow subgroups of symmetric groups

Abstract

Let p be any prime. Let Pn be a Sylow p-subgroup of the symmetric group Sn. Let ϕ and ψ be linear characters of Pn and let N be the normaliser of Pn in Sn. In this article we show that the inductions of ϕ and ψ to Sn are equal if, and only if, ϕ and ψ are N–conjugate. This is an analogue for symmetric groups of a result of Navarro for p-solvable groups.