Character formula for conjugacy classes in a coset

Tim Dokchitser*, Vladimir Dokchitser

*Corresponding author for this work

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

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 languageEnglish
Title of host publicationArithmetic of L-series
Subtitle of host publicationProceedings of International Conference in Madrid
PublisherAmerican Mathematical Society
Number of pages6
DOIs
Publication statusAccepted/In press - 15 Mar 2024

Publication series

NameEMS Series of Congress Reports
PublisherAmerican Mathematical Society
ISSN (Print)2523-515X
ISSN (Electronic)2523-5168

Keywords

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

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