Sharply transitive sets in PGL2(K)
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Sean Eberhard
Abstract
Here is a simplified proof that every sharply transitive subset of PGL2(K) is a coset of a subgroup, for every finite field K.
Funding statement: SE has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 803711).
Communicated by: T. Grundhöfer
References
[1] L. Bader, G. Lundardon, On the flocks of Q+(3, qGeom. Dedicata 29 (1989), 177–183. MR988267 Zbl 0673.5101010.1007/BF00182118Search in Google Scholar
[2] A. Bonisoli, The regular subgroups of the sharply 3-transitive finite permutation groups. In: Combinatorics ’86 (Trento, 1986), volume 37 of Ann. Discrete Math., 75–86, North-Holland 1988. MR931307 Zbl 0652.2000410.1016/S0167-5060(08)70227-9Search in Google Scholar
[3] A. Bonisoli, G. Korchmáros, Flocks of hyperbolic quadrics and linear groups containing homologies. Geom. Dedicata 42 (1992), 295–309. MR1164537 Zbl 0756.5100910.1007/BF02414068Search in Google Scholar
[4] N. Durante, A. Siciliano, (B)-geometries and flocks of hyperbolic quadrics. J. Combin. Theory Ser. A 102 (2003), 425–431. MR1979544 Zbl 1021.0501810.1016/S0097-3165(03)00044-XSearch in Google Scholar
[5] B. Segre, Ovals in a finite projective plane. Canadian J. Math. 7 (1955), 414–416. MR71034 Zbl 0065.1340210.4153/CJM-1955-045-xSearch in Google Scholar
[6] J. A. Thas, Flocks, maximal exterior sets, and inversive planes. In: Finite geometries and combinatorial designs (Lincoln, NE, 1987), volume 111 of Contemp. Math., 187–218, Amer. Math. Soc. 1990. MR1079748 Zbl 0728.5101010.1090/conm/111/1079748Search in Google Scholar
[7] J. A. Thas, Finite fields and Galois geometries. In: Finite fields and applications (Melbourne, Australia, 2007), volume 461 of Contemp. Math., 251–265, Amer. Math. Soc. 2008. MR2436341 Zbl 1176.0501610.1090/conm/461/08999Search in Google Scholar
[8] R. C. Valentini, M. L. Madan, A Hauptsatz of L. E. Dickson and Artin–Schreier extensions. J. Reine Angew. Math. 318 (1980), 156–177. MR579390 Zbl 0426.1201610.1515/crll.1980.318.156Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- An 𝔽p2-maximal Wiman sextic and its automorphisms
- Pseudo-algebraic Ricci solitons on Einstein nilradicals
- The wobbly divisors of the moduli space of rank-2 vector bundles
- Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
- Betti numbers and pseudoeffective cones in 2-Fano varieties
- The generating rank of a polar Grassmannian
- The Beckman–Quarles theorem via the triangle inequality
- On Huisman’s conjectures about unramified real curves
- Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
- On the Segre invariant for rank two vector bundles on ℙ2
- Lifting coarse homotopies
- How to construct all metric f-K-contact manifolds
- An extremum problem for the power moment of a convex polygon contained in a disc
- Sharply transitive sets in PGL2(K)
Articles in the same Issue
- Frontmatter
- An 𝔽p2-maximal Wiman sextic and its automorphisms
- Pseudo-algebraic Ricci solitons on Einstein nilradicals
- The wobbly divisors of the moduli space of rank-2 vector bundles
- Symmetries of complex analytic vector fields with an essential singularity on the Riemann sphere
- Betti numbers and pseudoeffective cones in 2-Fano varieties
- The generating rank of a polar Grassmannian
- The Beckman–Quarles theorem via the triangle inequality
- On Huisman’s conjectures about unramified real curves
- Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition
- On the Segre invariant for rank two vector bundles on ℙ2
- Lifting coarse homotopies
- How to construct all metric f-K-contact manifolds
- An extremum problem for the power moment of a convex polygon contained in a disc
- Sharply transitive sets in PGL2(K)
