A sharply 2-transitive group without a non-trivial abelian normal subgroup

Abstract

We show that any group $G$ is contained in some sharply 2-transitive group $\mathcal{G}$ without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups $\mathcal{G}$ that we construct have no fixed points.

13 pages, 7 figures, revised version