Speaker: Farideh Shafiei (Tehran)
Title: Taketa Inequality for Solvable Groups with Few Irreducible Character Degrees
Abstract:
Let \(G\) be a finite solvable group. As usual, we write \(dl(G)\) to denote the derived length of \(G\), and let \(cd(G)\) denote the set of degrees of irreducible characters of \(G\). It follows from an old result of Taketa when \(G\) is an \(M\)-group that \(dl(G) \leq cd(G)\), and it is conjectured that this Taketa inequality actually holds for all solvable groups. In this talk, I will survey on partial results regarding this conjecture including some of our results on verifying the conjecture for solvable groups with few irreducible character degrees.