Speaker: Martin Couson

Title: Character Degrees of Finite p-Groups by Coclass

Abstract: Let \((G_k \mid k \in \mathbb{N}_0)\) be a coclass family of finite \(p\)-groups and let \(l\) be a nonnegative integer. We show that there is a polynomial \(f_l \in \mathbb{Q}[X]\) with \(\deg(f_l) \leq d\), where \(d\) is the dimension of the associated pro-\(p\)-group, such that \(f_l(p^k) = \#\{ \chi \in \text{Irr}(G_k) \mid \chi(1) = p^l \}\) holds for every large enough \(k\).