2007/07/27 by Edith Adan-Bante, Adan-Bante, Edith
Computer Science · Mathematics · #20c15 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.0707.4184
openalex publication_date 2007/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite p-group, for some prime p, and ψ, θ∈ \Irr(G) be irreducible complex characters of G. It has been proved that if, in addition, ψ,θ are faithful characters, then the product ψθ is a multiple of an irreducible or it is the nontrivial linear combination of at least (p+1)/(2) distinct irreducible characters of G. We show that if we do not require the characters to be faithful, then given any integer k>0, we can always find a p-group G and irreducible characters Ψ and Θ such that ΨΘ is the nontrivial combination of exactly k distinct irreducible characters. We do this by translating examples of decompositions of restrictions of characters into decompositions of products of characters.