Suggestions about the set of all irreducible complex character degrees of a finite group

Question

Let $G$ be a finite group, $\operatorname{cd}(G)$ be the set of all irreducible complex character degrees of $G$, and $\rho(G)$ be the set of all prime divisors of integers in $\operatorname{cd}(G)$. For a prime $p$ and a positive integer $n$, the $p$-part of $n$, denoted by $n_p$, is the maximum power of $p$ such that $n_p \mid n$. We are interested in studying the set $V(G)=\{p^{e_p(G)} \mid p \in \rho(G)\}$, where $p^{e_p(G)}=\max \{n_p \mid n \in \operatorname{cd}(G)\}$, and its impact on the structure of the group $G$. However, we lack a good reference for this. We would appreciate any suggestions.

Answer 1

Here are some references:

Itô-Michler Theorem. N. Itô: Some studes on group characters (Nagoya 1951) G. O. Michler: Brauer's conjectures and the classification of finite simple groups (Springer LNM1178, 1986)

Hung & Tiep: The average character degree and an improvement on the Itô-Michler theorem (J Algebra 2020)

Navarro: Variations on the Itô-Michler Theorem on character degrees (Rocky Mountain 2016)

These contain further references you can chase up.