10 problems

Bauer–Catanese–Grunewald conjecture. Every non-abelian finite simple group other than $A_5$ is a Beauville group.

Boston's conjecture. The groups

Let $p$ be a prime, and consider the two non-isomorphic groups of order $p^5$ denoted by $H_3$ and $H_4$ in the cited source. Conjecture on Beauville groups of order $p^5$. For…

Let $K_1$ and $K_2$ be finite Coxeter groups. A Beauville group is a finite group admitting a Beauville structure, and a Beauville structure is strongly real if it is inverted by a…

Let $G$ be a simple group and let $E$ be a split extension of $G$. A Beauville group is a group admitting a Beauville structure, and a strongly real Beauville group is one admittin…

Let $H$ be a finite simple group of order greater than $3$. Direct-square conjecture. The direct product $H\times H$ is a strongly real Beauville group. This is presented as a more…

Let $G$ be a non-abelian finite simple group. A strongly real Beauville group is a Beauville group admitting a Beauville structure with the strong reality property. Exceptional-gro…

A finite group is strongly real Beauville if it is a Beauville group whose Beauville structure satisfies the relevant strong reality condition. Finiteness conjecture. All but finit…

Let $G$ be a finite simple group. A mixable Beauville group is a perfect group with elements $x1,y1,x2,y2 eq$ necessarily distinct such that $o(x1)$ and $o(y1)$ are even,…

Let $p$ be a prime, let $g(p)$ denote the number of Beauville $p$-groups of order $p^{5}$, and let $H_3$ and $H_4$ be the groups referred to in the preceding construction. The Beau…