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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References
R. Guralnick and P. H. Tiep, The non-coprime k(GV)-problem, Journal of Algebra 279 (2004), 694–719.
I. M. Isaacs, Character theory of finite groups, Academic Press, New York, 1976.
T. M. Keller, Fixed conjugacy classes of normal subgroups and the k(GV)-problem, Journal of Algebra 305 (2006), 457–486.
R. Knörr, On the number of characters in a p-block of a p-solvable group, Illinois Journal of Mathematics 28 (1984), 181–209.
G. R. Robinson, A bound on norms of generalized characters with applications, Journal of Algebra 212 (1999), 660–668.
P. Schmid, Some remarks on the k(GV)-theorem, Journal of Group Theory 8 (2005), 589–604.
P. Schmid, The solution of the k(GV) problem, ICP Advanced Texts in Mathematics, 4. Imperial College Press, London, 2007.
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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