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Elations of Designs

Published online by Cambridge University Press:  20 November 2018

William M. Kantor
William M. Kantor*
Affiliation:
University of Illinois, Chicago, Illinois
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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].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 897 - 904
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Dembowski, P., Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44 (Springer-Verlag, New York, 1968).Google Scholar
2. Kantor, W. M., Characterizations of finite projective and affine spaces, Can. J. Math. 21 (1969), 64–75.Google Scholar
3. Kantor, W. M., Jordan groups, J. Algebra 12 (1969), 471–493.Google Scholar
4. Liineburg, H., Zentrale Automorphismen von-Raumen, Arch. Math. 12 (1961), 134–145.Google Scholar