3 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…

Let $G$ be a finite group, let $p$ be a prime, let $P$ be a Sylow $p$-subgroup of $G$, and let $\chi\in\operatorname{Irr}(G)$. For a subgroup $Q\le P$, write $\chi(1)_p$ for the…

Let $p$ be a prime, let $G$ be a $p$-solvable finite group, and let $P$ be a Sylow $p$-subgroup of $G$. Let $\operatorname{N}_{G}(P)$ be the normalizer of $P$, and let…