2005/04/28 by Thomas Michael Keller, Keller, Thomas Michael
Computer Science · Engineering · Mathematics · #20B05 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems #math.GR #math.RT #msc:20B05
paper · pdf · doi:10.48550/arxiv.math/0504574
arxiv created 2005/04/28 · openalex publication_date 2005/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish several new bounds for the number of conjugacy classes of a finite group, all of which involve the maximal number c of conjugacy classes of a normal subgroup fixed by some element of a suitable subset of the group. To apply these formulas effectively, the parameter c, which in general is hard to control, is studied in some important situations. These results are then used to provide a new, shorter proof of the most difficult case of the well-known k(GV)-problem, which occurs for p=5 and V induced from the natural module of a 5-complement of GL(2,5). We also show how, for large p, the new results reduce the k(GV)-problem to the primitive case, thereby improving previous work on this. Furthermore, we discuss how they can be used in tackling the imprimitive case of the as of yet unsolved noncoprime k(GV)-problem.