Linear characters of Sylow subgroups of symmetric groups

Eugenio Giannelli; Stacey Law; Jason Long

doi:10.1016/j.jalgebra.2021.04.036

Linear characters of Sylow subgroups of symmetric groups

Eugenio Giannelli, Stacey Law^*, Jason Long

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let p be any prime. Let P_nbe a Sylow p-subgroup of the symmetric group G_n. Let ϕ and ψ be linear characters of P_n and let N be the normaliser of P_nin G_n. In this article we show that the inductions of ϕ and ψ to G_nare 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.

Original language	English
Pages (from-to)	125-160
Number of pages	36
Journal	Journal of Algebra
Volume	584
Early online date	2 Jun 2021
DOIs	https://doi.org/10.1016/j.jalgebra.2021.04.036
Publication status	Published - 15 Oct 2021

Bibliographical note

Acknowledgements:
We thank the anonymous reviewer for his/her helpful corrections. The second author was supported by a London Mathematical Society Early Career Fellowship at the University of Oxford (ECF-1819-05).

Keywords

Linear characters
Sylow subgroups
Symmetric groups

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title = "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 Gn. Let ϕ and ψ be linear characters of Pn and let N be the normaliser of Pn in Gn. In this article we show that the inductions of ϕ and ψ to Gn 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.",

keywords = "Linear characters, Sylow subgroups, Symmetric groups",

author = "Eugenio Giannelli and Stacey Law and Jason Long",

note = "Acknowledgements: We thank the anonymous reviewer for his/her helpful corrections. The second author was supported by a London Mathematical Society Early Career Fellowship at the University of Oxford (ECF-1819-05).",

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T1 - Linear characters of Sylow subgroups of symmetric groups

AU - Giannelli, Eugenio

AU - Law, Stacey

AU - Long, Jason

N1 - Acknowledgements: We thank the anonymous reviewer for his/her helpful corrections. The second author was supported by a London Mathematical Society Early Career Fellowship at the University of Oxford (ECF-1819-05).

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Y1 - 2021/10/15

N2 - Let p be any prime. Let Pn be a Sylow p-subgroup of the symmetric group Gn. Let ϕ and ψ be linear characters of Pn and let N be the normaliser of Pn in Gn. In this article we show that the inductions of ϕ and ψ to Gn 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.

AB - Let p be any prime. Let Pn be a Sylow p-subgroup of the symmetric group Gn. Let ϕ and ψ be linear characters of Pn and let N be the normaliser of Pn in Gn. In this article we show that the inductions of ϕ and ψ to Gn 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.

KW - Linear characters

KW - Sylow subgroups

KW - Symmetric groups

U2 - 10.1016/j.jalgebra.2021.04.036

DO - 10.1016/j.jalgebra.2021.04.036

M3 - Article

SN - 0021-8693

VL - 584

SP - 125

EP - 160

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Linear characters of Sylow subgroups of symmetric groups

Abstract

Bibliographical note

Keywords

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