Sharply 2-transitive linear groups

Sharply 2-transitive groups are groups that admit a transitive and free action on pairs of distinct points. Finite sharply 2-transitive groups have been thoroughly studied, and completely classified by H. Zassenhaus in the 1930’s, but up to some few years back, relatively little was known about the infinite case. In this lecture we will survey the latest developments regarding infinite sharply 2-transitive groups, and present our results in this field.