7 problems

Let $\mathcal{H}$ be the class of finite groups satisfying … and let Theorem … . It might also contain simple and nonsimple groups that do not necessarily possess a nontrivial part…

Let $G$ be a finite non-solvable group. For a positive integer $n$, call $G$ an $S^{n}$-group if it has exactly $n$ non-nilpotent subgroups. Zarrin's conjecture. If $G$ is an…

Consider the class of two-dimensional shallow water equations with variable bottom topography, denoted by $\mathcal L$, and its spaces of zeroth-order conservation laws. Two cases…

Distinct-count conjecture for $\Gamma(k)$. The numbers $|Sup(G)|$ are distinct for all members $G$ of $\Gamma(k)$ if and only if $k=6$. When $k=6$, the groups are

Let $G$ be a simple group of finite Morley rank definable in a Zariski geometry. Zariski-geometry algebraicity conjecture. The group $G$ has a Lie algebra and is a simple algebraic…

Let $G$ be a simple group of finite Morley rank admitting a generically $4$-transitive action. Generically 4-transitive classification conjecture. Either…

Let $p$ be a prime and let $G$ be a finite group with ${\mathbf{O}}_p(G)=1$. A group has four $p$-regular classes when $k_{p'}(G)=4$, where $k_{p'}(G)$ denotes the number of conjug…