A characterization ofL n(K) as a permutation group

In 1972 M. O'Nan proved thatL_n (q),h 3; can be characterized as a doubly-transitive groupG on a finite set , whereG_a has an Abelian normal subgroup acting not semi-regularly on -a. In the Main Theorem we show that a similar statement holds if is infinite. Our result implies O'Nan's theorem.This paper is part of the author's Ph.D. thesis written under supervision of Prof. F. G. Timmesfeld.