On the planes of Suetake
Tóm tắt
The Suetake planes and the simple full non-square André planes are shown to be exactly those finite translation planes that are coupled with a semifield plane. Also, the Suetake planes are never generalized André planes.
Tài liệu tham khảo
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Cordero, M., Figueroa, R.: Transitive autotopism groups and the generalized twisted field planes. In: Johnson, N.L. (ed.) Mostly Finite Geometries. Lecture Notes in Pure and Applied Mathematics, vol. 190, pp. 191–196. Marcel Dekker, New York (1997)
Foulser D.A.: A generalization of André’s systems. Math. Z. 100, 380–395 (1967)
Ganley M.J., Jha V.: On translation planes with a 2-transitive orbit on the line at infinity. Arch. Math. 47, 197–208 (1986)
Ganley M.J., Jha V., Johnson N.L.: The translation planes admitting a nonsolvable doubly transitive line-sized orbit. J. Geom. 69, 88–109 (2000)
Suetake C.: A family of translation planes of order q 2m+1 with two orbits of lengths 2 and q 2m+1 – 1 on L ∞. Geom. Dedicata 42, 163–185 (1992)