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Elations of Designs

  • William M. Kantor (a1)

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An elation of a design is an automorphism γ of fixing some block X pointwise and some point x on X blockwise. Luneburg [4] and I [2] have proved results which state that a design admitting many dations and having additional properties must be the design of points and hyperplanes of a finite desarguesian projective space. In this note, additional results of this type will be proved and applied to yield a generalization of a previous result on Jordan groups [3]. The proofs were suggested by a result of Hering on dations of finite projective planes [1, pp. 122, 190].

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References

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1. Dembowski, P., Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44 (Springer-Verlag, New York, 1968).
2. Kantor, W. M., Characterizations of finite projective and affine spaces, Can. J. Math. 21 (1969), 6475.
3. Kantor, W. M., Jordan groups, J. Algebra 12 (1969), 471493.
4. Liineburg, H., Zentrale Automorphismen von-Raumen, Arch. Math. 12 (1961), 134145.
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Elations of Designs

  • William M. Kantor (a1)

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