Abstract
Let G be a finite group and V be a finite G-module. We present upper bounds for the cardinalities of certain subsets of Irr(GV), such as the set of those χ ∈ Irr(GV) such that, for a fixed v ∈ V, the restriction of χ to 〈v〉 is not a multiple of the regular character of 〈v〉. These results might be useful in attacking the noncoprime k(GV)-problem.
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Keller, T.M. Counting characters in linear group actions. Isr. J. Math. 171, 367–384 (2009). https://doi.org/10.1007/s11856-009-0054-5
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DOI: https://doi.org/10.1007/s11856-009-0054-5