A group Γ 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, see Definition 2) such that. This is well known in the finite case. We prove this conjecture when Γ<GLn(F) is a linear group, where F is any field with char(F)≠2 and that p-char(Γ)≠2 (see Definition 2.2).
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