3 problems

Let $G$ be an almost simple group, meaning that $T\leq G\leq {\rm Aut}(T)$ for some non-abelian finite simple group $T$, and let $H$ be a maximal subgroup of $G$. Write $d(H)$ for…

Let $S$ be a finite nonabelian simple group. A finite group $G$ is isospectral to $S$ if they have the same sets of element orders, $(G)=(S)$. A group is almost simple with socle…

Conder's conjecture. The integer $\mu_G(1)$ is divisible by $|N|$.