A nearfield-free definition of regular Hughes planes and some embeddings of PG(3,q) in Hughes planes of order q
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Authors: | Julia M N Brown |
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Institution: | (1) Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, Canada, M3J 1P3 |
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Abstract: | We give a nearfield-free definition of some finite and infinite incidence systems by means of half-points and half-lines and
show that they are projective planes. We determine a planar ternary ring for these planes and use it to determine the full
collineation group and to demonstrate some embeddings of these planes among themselves. We show that these planes include
all finite regular Hughes planes and many infinite ones. We also show that PG(3, q) embeds in Hu(q
4) (and show infinite versions of this embedding).
Dan Hughes 80th Birthday. |
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Keywords: | Regular Hughes planes Half-point Half-line Planar ternary ring Embedding of PG(3 q) |
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