  A group G is sharply 2-transitive if it admits a faithful permutation
representation that is transitive and free on pairs of distinct points.
Conjecturally, for all such groups there exists a near-field N (i.e. a skew
field that is distributive only from the left) such that G is isomorphic to the
semidirect product of the multiplicative and additive groups of N. This is well
known in the finite case. We prove this conjecture when G < GL(n,F) is a linear
group. Here we have to assume that both the characteristic of the field F and
the permutational characteristic of the group G (see Definition 2.1) are not
equal to 2.
