Doubly Transitive Automorphism Groups of Combinatorial Surfaces

The combinatorial surfaces with doubly transitive automorphism groups are classified. This is established by classifying the automorphism groups of combinatorial surfaces which act doubly transitively on the vertices of the surface. The doubly transitive automorphism groups of combinatorial surfaces are the symmetric group S4 , the alternating group A5 and the Frobenius group C7 (dot) C6 . In each case the combinatorial surface is uniquely determined. The symmetric group S4 acts doubly transitively on the tetrahedron surface, the alternating group A5 on the triangulation of the projective plane with six vertices and the Frobenius group C7 (dot) C6 on the Moebius torus with seven vertices. [PUBLICATION ABSTRACT]