9 problems

Let $p$ be a prime, let $G$ be a $p$-solvable group, and let $\varphi\in\operatorname{IBr}(G)$ be an irreducible Brauer character. A lift of $\varphi$ is a character…

Prime-graph complement characterization. For every strictly $T$-solvable group $G$, there exists a set $Y\subseteq\bigcup_{p\in\pi(T)}\operatorname{IBr}_p(T)$ such that

Navarro's conjecture.

Let $G$ be a finite quasi-simple group with centre $Z(G)$ of $p'$-order. Let $\operatorname{IBr}(G\mid\theta)$ denote the irreducible $p$-Brauer characters of $G$ lying over…

Let $G$ be a finite group and let $p$ be a prime. Write $|G|_{p'}$ for the prime-to-$p$ part of the order of $G$, and let $\operatorname{IBr}(G)$ denote the irreducible $p$-Brauer…

Counting conjecture. Suppose that $p$ is good for $\mathbf{G}$. Then $\alpha_\ell$ is the number of unipotent irreducible Brauer characters of $G$.

Let $G$ be a finite group, let $p$ be a prime, and let $\chi\in\operatorname{Irr}(G)$. Let $\chi^0$ be the restriction of $\chi$ to the elements of $G$ of order prime to $p$, and l…

The Brauer degree-square conjecture. One always has

The norm inequality. The inequality