2 problems

Let $G$ be a finite simple group and let $H\leq G$ be a subgroup of odd index. A subgroup $H$ is pronormal in $G$ if, for every $g\in G$, $H$ and $H^g$ are conjugate in…

Let $G=PSL_n^\varepsilon(q)$, where $q$ is odd and $\varepsilon\in\{+,-\}$. For positive integers $m,n$, write $m\prec n$ for the relation used in the source. A subgroup of $G$ has…