A Generalization of a Result of L. Baumert and M. Hall About Projective Planes of Order 12
نویسندگان
چکیده
In [ 1 ] it was shown that there is no projective plane of order 12 which possesses a collineation group of order 12 consisting of elations with a fixed point as a center and a fixed line as its axis. We prove THEOREM A. There is no projective plane of order 12 which possesses a collineation group of order 4 consisting of elations with a fixed point as a center and a fixed line as its axis. Proof Let P be a projective plane of order 12 with a collineation group G of order 4 consisting of elations with a fixed point 0 as a center and a fixed line o as its axis. We have 0 E o and we may set For the other 12 lines through 0 we may set PI= (05 (lO)j, (lI)jY (12)j/j=O3 l3 253\ P2= (0, (2fJ)j, the 36 nontrivial G-orbits of points. The " outer " indices j = 0, 1, 2, 3 are considered as integers mod 4. We shall also write ijk for (ij)k.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 32 شماره
صفحات -
تاریخ انتشار 1982