| Summary: | This thesis provides a complete answer to the question: What are the Collineation Groups G of a Finite Projective Space S which are Doubly Transitive on the points of S. This problem was first proposed by A. WAGNERin 1961 and later explored by W. KANTORin 1973. Many geometrical incidence structures are examined in the course of the proof of the main theorem M*: Let G be a Doubly Transitive Collineation Group on the Finite Space Sk, q with 1#k. Then G contains a normal subgroup H isomorphic to PSL(k+l, q) unless (k, q) = (3,2) when H may be the Alternating Group A7. X is aT group on Sd means X acts transitively on the non-incident point, hyperplane pairs of Sd. Chapter One ends with the following minor theorem: If X is a primitive linear T group on Sd, X not 2-transitive on Sd then X is some subgroup of the Symplectic Group PSp (d+l,q).
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