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- W2073104231 abstract "We investigate collineation groups of a finite projective plane of odd order fixing an oval and having two orbits on it, one of which is assumed to be primitive. The situation in which there exists a fixed triangle off the oval is considered in detail. Our main result is the following. Theorem. Let π be a finite projective plane of odd order n containing an oval Ω. If a collineation group G of π satisfies the properties: G fixes Ω and the action of G on Ω yields precisely two orbits Ω1 and Ω2, G has even order and a faithful primitive action on Ω2, G fixes neither points nor lines but fixes a triangle ABC in which the points A, B, C are not on the oval Ω, Each order n∈{7,9,27} does furnish at least one example for the above situation; the determination of the planes and the groups which do occur is complete for n=7, 9; the determination of the planes is still incomplete for n=27." @default.
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- W2073104231 date "2003-05-01" @default.
- W2073104231 modified "2023-09-23" @default.
- W2073104231 title "Intransitive collineation groups of ovals fixing a triangle" @default.
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- W2073104231 doi "https://doi.org/10.1016/s0097-3165(03)00011-6" @default.
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