@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 = "2024",

month = mar,

day = "15",

doi = "10.48550/arXiv.2105.07247",

language = "English",

series = "EMS Series of Congress Reports",

publisher = "American Mathematical Society",

booktitle = "Arithmetic of L-series",

address = "United States",

}