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.
Linear characters of Sylow subgroups of symmetric groups / Giannelli E.; Law S.; Long J.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 584:(2021), pp. 125-160. [10.1016/j.jalgebra.2021.04.036]
Linear characters of Sylow subgroups of symmetric groups
Giannelli E.;
2021
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.
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