11.52 (1990)

(Well-known problem). A permutation group on a set $\Omega$ is called sharply doubly transitive if for any two pairs $(\alpha, \beta)$ and $(\gamma, \delta)$ of elements of $\Omega$ such that $\alpha \neq \beta$ and $\gamma \neq \delta$, there is exactly one element of the group taking $\alpha$ to $\gamma$ and $\beta$ to $\delta$. Does every sharply doubly transitive group possess a non-trivial abelian normal subgroup?