A characterization of PGL(2, q), q odd

Rinaldi, Gloria

doi:10.1007/bf00181338

Cited by 2 publications

(1 citation statement)

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“…We also want to remark that characterizations of PGL(2, q), q a prime power, among the finite sharply 3-transitive sets have been given in terms of certain subsets of involutions of these sets (see [BK1,Theorem 1;BK2;FK;and Ri,Theorem]). Incidence structures of fixed-point and fixed-circle sets of special kinds of automorphisms of Minkowski planes have already been investigated (see [QR]).…”

Section: All Real Abstract Ovals Are Projectivementioning

confidence: 99%

Invertible Sharplyn-Transitive Sets

Polster

1998

Journal of Combinatorial Theory, Series A

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We prove various results about sharply n-transitive sets of homeomorphisms of`n ice'' topological spaces like the real line and the circle. Our main results concern sharply 3-transitive sets G of homeomorphisms of the circle to itself. If G=G &1 , then G contains a real hyperbolic part (a set of involutions of the circle having special properties). We show that every real hyperbolic part is the hyperbolic part of a real abstract oval in the sense of Buekenhout and that every real abstract oval arises from a topological oval in a flat projective plane. This establishes a new relationship between flat Minkowski planes that admit automorphisms which are circle-symmetries and flat projective planes containing topological ovals. We also consider sharply n-transitive sets of permutations acting on finite sets. We find that our results about flat geometries and sharply n-transitive sets of homeomorphisms have counterparts in the finite case.

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Section: All Real Abstract Ovals Are Projectivementioning

confidence: 99%