11 problems

Lisi–Sabatini conjecture for simple groups. There exists an element $x \in G$ such that

Lisi–Sabatini conjecture. There exists an element $x \in G$ such that, for each $i$, $P_i \cap P_i^x$ is inclusion-minimal in the set

For a prime $p$, let $O_p(G)$ be the intersection of all Sylow $p$-subgroups of $G$. Say that $G$ has $(*)_p$ if there exist two Sylow $p$-subgroups whose intersection is contained…

Fix a prime $p$. Let $G\unlhd A$ be finite groups, let $P$ be a Sylow $p$-subgroup of $G$, and write $\operatorname{IBr}(H)$ for the set of $p$-Brauer characters of a group $H$. Sy…

Let $G$ be a finite group, let $p$ be a prime, and let $P$ be a Sylow $p$-subgroup of $G$. Write $\operatorname{IBr}(G)$ for the set of $p$-Brauer characters of $G$. Malle–Navarro–…

Let $p$ be an odd prime, and let $G$ be a finite group with subgroup $H$. For a finite group $X$, write $up(X)$ for the number of Sylow $p$-subgroups of $X$. **Gap conjecture for…

Let $G$ be a finite group, and let $v_p(G)$ denote the number of Sylow $p$-subgroups of $G$. Robinson's solvability conjecture. If … for each odd prime number $p$, then $G$ is solv…

Let $G$ be a finite group and let $P$ be a Sylow $2$-subgroup of $G$, with $4\mid |G|$. Let $B_0(G)$ be the principal $2$-block, and let…

Let $G$ be a finite group and let $P\in\operatorname{Syl}_2(G)$. Let $\sigma\in\operatorname{Gal}(\mathbb{Q}^{\mathrm{ab}}/\mathbb{Q})$ be the unique automorphism that fixes $2$-ro…

Let $G$ be a finite group and let $P\in\operatorname{Syl}_2(G)$. Let $\sigma\in\operatorname{Gal}(\mathbb{Q}^{\mathrm{ab}}/\mathbb{Q})$ be the unique automorphism that fixes $2$-ro…

Almost simple group conjecture. If $S$ satisfies $\mathbf{DivSyl}(p)$, then every group $L$ satisfying