Dokchitser, Tim;
Dokchitser, Vladimir;
(2025)
Character formula for conjugacy classes in a coset.
In: Bullach, Dominik and Macías Castillo, Daniel, (eds.)
Arithmetic of L-Functions: Proceedings of an International Conference.
(pp. 93-100).
EMS Press: Berlin, Germany.
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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.
| Type: | Book chapter |
|---|---|
| Title: | Character formula for conjugacy classes in a coset |
| ISBN-13: | 978-3-98547-084-6 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4171/ECR/20/3 |
| Publisher version: | https://doi.org/10.4171/ECR/20/3 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Finite groups; conjugacy classes; characters; quotient group |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10205335 |
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