Character formula for conjugacy classes in a coset

Tim Dokchitser; Vladimir Dokchitser

doi:10.4171/ECR/20/3

Character formula for conjugacy classes in a coset

Tim Dokchitser^*, Vladimir Dokchitser

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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Abstract

Let G be a finite group and N<G a normal subgroup with G/N abelian. We show how the conjugacy classes of G in a given coset qN relate to the irreducible characters of G that are not identically 0 on qN. We describe several consequences. In particular, we deduce that when G/N is cyclic generated by q, the number of irreducible characters of N that extend to G is the number of conjugacy classes of G in qN.

Original language	English
Title of host publication	Arithmetic of L-Functions
Subtitle of host publication	Proceedings of an International Conference held at ICMAT, Madrid, May 2023
Publisher	American Mathematical Society
Pages	93-100
Number of pages	8
ISBN (Electronic)	9783985475841
ISBN (Print)	9783985470846
DOIs	https://doi.org/10.4171/ECR/20/3
Publication status	Published - 3 Mar 2025
Event	International conference on the Arithmetic of L‐functions - Instituto de Ciencias Matemáticas, Madrid, Spain Duration: 22 May 2023 → 26 May 2023 https://www.icmat.es/congresos/2023/AOLF/index.php

Publication series

Name	EMS Series of Congress Reports
Publisher	American Mathematical Society
ISSN (Print)	2523-515X
ISSN (Electronic)	2523-5168

Conference

Conference	International conference on the Arithmetic of L‐functions
Country/Territory	Spain
City	Madrid
Period	22/05/23 → 26/05/23
Internet address	https://www.icmat.es/congresos/2023/AOLF/index.php

Keywords

math.GR
20C15, 20E45 (Primary), 20C25, 20K35 (Secondary)

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Accepted author manuscript, 298 KBLicence: CC BY

https://arxiv.org/abs/2105.07247Licence: CC BY

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@inproceedings{f552f645b89c43d0afacbd28767302ab,

title = "Character formula for conjugacy classes in a coset",

abstract = "Let G be a finite group and N<G a normal subgroup with G/N abelian. We show how the conjugacy classes of G in a given coset qN relate to the irreducible characters of G that are not identically 0 on qN. We describe several consequences. In particular, we deduce that when G/N is cyclic generated by q, the number of irreducible characters of N that extend to G is the number of conjugacy classes of G in qN.",

keywords = "math.GR, 20C15, 20E45 (Primary), 20C25, 20K35 (Secondary)",

author = "Tim Dokchitser and Vladimir Dokchitser",

year = "2025",

month = mar,

day = "3",

doi = "10.4171/ECR/20/3",

language = "English",

isbn = " 9783985470846",

series = "EMS Series of Congress Reports",

publisher = "American Mathematical Society",

pages = "93--100",

booktitle = "Arithmetic of L-Functions",

address = "United States",

note = "International conference on the Arithmetic of L‐functions ; Conference date: 22-05-2023 Through 26-05-2023",

url = "https://www.icmat.es/congresos/2023/AOLF/index.php",

}

Dokchitser, T & Dokchitser, V 2025, Character formula for conjugacy classes in a coset. in Arithmetic of L-Functions: Proceedings of an International Conference held at ICMAT, Madrid, May 2023. EMS Series of Congress Reports, American Mathematical Society, pp. 93-100, International conference on the Arithmetic of L‐functions, Madrid, Spain, 22/05/23. https://doi.org/10.4171/ECR/20/3

Character formula for conjugacy classes in a coset. / Dokchitser, Tim; Dokchitser, Vladimir.
Arithmetic of L-Functions: Proceedings of an International Conference held at ICMAT, Madrid, May 2023. American Mathematical Society, 2025. p. 93-100 (EMS Series of Congress Reports).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

TY - GEN

T1 - Character formula for conjugacy classes in a coset

AU - Dokchitser, Tim

AU - Dokchitser, Vladimir

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N2 - Let G be a finite group and N<G a normal subgroup with G/N abelian. We show how the conjugacy classes of G in a given coset qN relate to the irreducible characters of G that are not identically 0 on qN. We describe several consequences. In particular, we deduce that when G/N is cyclic generated by q, the number of irreducible characters of N that extend to G is the number of conjugacy classes of G in qN.

AB - Let G be a finite group and N<G a normal subgroup with G/N abelian. We show how the conjugacy classes of G in a given coset qN relate to the irreducible characters of G that are not identically 0 on qN. We describe several consequences. In particular, we deduce that when G/N is cyclic generated by q, the number of irreducible characters of N that extend to G is the number of conjugacy classes of G in qN.

KW - math.GR

KW - 20C15, 20E45 (Primary), 20C25, 20K35 (Secondary)

UR - https://www.icmat.es/congresos/2023/AOLF/index.php

U2 - 10.4171/ECR/20/3

DO - 10.4171/ECR/20/3

M3 - Conference Contribution (Conference Proceeding)

SN - 9783985470846

T3 - EMS Series of Congress Reports

SP - 93

EP - 100

BT - Arithmetic of L-Functions

PB - American Mathematical Society

T2 - International conference on the Arithmetic of L‐functions

Y2 - 22 May 2023 through 26 May 2023

ER -

Character formula for conjugacy classes in a coset

Abstract

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Keywords

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