论文信息 - A Projective Plane of Order 16

A Projective Plane of Order 16

Abstract A projective plane of order 16 is constructed. It is a translation plane and appears to be new. The representation of the collineation group on the axis of the plane has a normal subgroup isomorphic to L 3 (2) with factor group isomorphic to S 3 . The orbits of this representation have lengths 14 and 3. If two points in the latter orbit are chosen to define a sharply doubly transitive set of permutations, the permutations from the multiplicative loop generate a group isomorphic to A 7 . The plane is of Lenz-Barlotti class IVa.1.

Peter Lorimer | P. Lorimer

[1] D. A. Foulser. A generalization of André's systems , 1967 .

[2] A. Wagner,et al. On collineation groups of projective spaces. I , 1961 .

[3] L. Dickson. Linear Groups, with an Exposition of the Galois Field Theory , 1958 .

[4] T. Ostrom,et al. Finite Translation Planes , 1970 .

[6] Erwin Kleinfeld. Techniques for Enumerating Veblen-Wedderburn Systems , 1960, JACM.

[7] David Perin,et al. On collineation groups of finite projective spaces , 1972 .

[8] David A. Foulser,et al. Solvable flag transitive affine groups , 1964 .