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Finite Projective Geometries

Published online by Cambridge University Press:  20 November 2018

Gerald Berman
Gerald Berman*
Affiliation:
Illinois Institute of Technology
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James Singer [12] has shown that there exists a collineation which is transitive on the (t - 1)-spaces, that is, (t - 1)-dimensional linear subspaces, of PG(t, pn). In this paper we shall generalize this result showing that there exist t - r collineations which together are transitive on the s-spaces of PG(t, pn). An explicit construction will be given for such a set of collineations with the aid of primitive elements of Galois fields. This leads to a calculus for the linear subspaces of finite projective geometries.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 4 , 1952 , pp. 302 - 313
Copyright
Copyright © Canadian Mathematical Society 1952

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