10 problems

Classification conjecture. $C$ is equivalent to one of the codes described in parts 1, 3, 4 or 5 of the main result.

Nagell's conjecture. The group $G$ must be of affine or almost simple type.

Let $G$ be a group acting point-primitively on the points of a generalised quadrangle $\mathcal{Q}$. The lines of $\mathcal{Q}$ are the objects on which $G$ acts, and a line-orbit…

Let $\mathcal{Q}$ be a thick finite generalised quadrangle, and let $G$ be a collineation group of $\mathcal{Q}$ acting primitively on its point set. Affine-or-almost-simple conjec…

An AS-configuration is a group $G$ of order $q^3$ together with subgroups $U_0,U_1,\ldots,U_{q+1}$, each of order $q$, such that $U_0$ is normal in $G$ and $U_iU_j\cap U_k=\\{1\\}$…

Let $\mathcal{Q}$ be a finite thick generalised quadrangle and let $G$ be a group of automorphisms acting regularly on the set of points. Point-regular automorphism group classific…

Heisenberg group conjecture. Then $G$ is isomorphic to a Heisenberg group of dimension $3$ over $\mathrm{GF}(q)$, where $q$ is a power of $p$. The groups $P$ for $q=3^f$ and…

Let $\mathcal{Q}$ be a generalised quadrangle admitting a group of automorphisms $G$ acting regularly on its points. Let $s$ denote the relevant order parameter, let $\mathcal{Q}'$…

Hemisystem difference conjecture. The set

Classification conjecture. If $\mathcal{I}$ is a negative intriguing set of $\mathcal{G}\setminus P^\perp$, then either there are points $Z_1,\ldots,Z_n$ of $P^\perp$ such that