3 problems

Let $G$ be a finite group, and let $\mathbf F(G)$ denote its Fitting subgroup. Write $\operatorname{Irr}(G)$ for the set of irreducible characters of $G$. Four-character Fitting-in…

Let $G$ be a finite group, and let $\rho(G)$ be the set of primes dividing the degree of some irreducible character of $G$. Write $\operatorname{Irr}(G)$ for the set of irreducible…

Let $G$ be a finite group of Lie type with Weyl group ${\mathbf{W}}$ and Frobenius-induced automorphism $\gamma$, defined over a field with parameter $q$, and let $k$ be a field of…