6 problems

Let $G$ be a finite group, and let $\mathbf F(G)$ denote its Fitting subgroup. Let $b(G)$ be the largest degree of the irreducible characters of $G$. Gluck's conjecture. If $G$ is…

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…

For each $n$, write $\lambda\vdash n$ for a partition of $n$, and let $\chi^\lambda$ be the corresponding irreducible character of $S_n$. Define its degree by…

Bounded-largest-degree multiplicity conjecture. The sequence

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…