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- W2085914150 abstract "Let G be an irreducible collineation group of a finite projective plane π of even order n≡0mod4. Our goal is to determine the structure of G under the hypothesis that G fixes a hyperoval Ω of π. We assume |G|≡0mod4. If G has no involutory elation, then G=O(G)⋊S2 with a cyclic Sylow 2-subgroup S2 and G has a normal subgroup M of odd order such that a G/M has a minimal normal 3-subgroup. If the subgroup S generated by all involutory elations in G is non-trivial and Z(S) denotes its center, then either S≅Alt(6) and n=4, or S/Z(S)≅(C3×C3)⋊C2, Z(S) is a (possibly trivial) 3-group and n≡1mod3. In the latter case there exists a G-invariant subplane π̃ in π such that the collineation group G induced by G on π̃ is irreducible and fixes a hyperoval Ω. Furthermore, the subgroup S generated by all involutory elations in G is a generalized Hessian group of order 18, that is S≅(C3×C3)⋊C2 and the configuration of the centers of the involutory elations in G consists of the nine inflexions of an equianharmonic cubic of a subplane π0 of order 4. In particular, π0 is generated by the centers and the axes of all involutory elations in G, and hence it is the so-called Hering's minimal subplane of π with respect to G." @default.
- W2085914150 created "2016-06-24" @default.
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- W2085914150 date "2002-06-01" @default.
- W2085914150 modified "2023-10-16" @default.
- W2085914150 title "Irreducible collineation groups fixing a hyperoval" @default.
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- W2085914150 doi "https://doi.org/10.1016/s0021-8693(02)00058-3" @default.
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