Abstract
A sharply 2-transitive subset of a permutation group G acting on a set Σ is a subset R of G with the properties
-
(1)
if α, β, γ, δ ∈ Σ, α ≠ β, γ ≠ δ, R contains a unique member r with r(α) = γ, r(β) = δ,
-
(2)
1 ∈ R,
-
(3)
the relation ~ defined on R by r ~ s if r = s or r −1 s fixes no symbol of Σ is an equivalence relation and each equivalence class is sharply transitive on Σ, that is, if α, γ ∈ Σ each class contains exactly one member r with r(α) = γ.
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Lorimer, P. (1974). Finite Projective Planes and Sharply 2-Transitive Subsets of Finite Groups. In: Newman, M.F. (eds) Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21571-5_43
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DOI: https://doi.org/10.1007/978-3-662-21571-5_43
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