Finite Projective Geometries
- 1 January 1952
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 4, 302-313
- https://doi.org/10.4153/cjm-1952-027-5
Abstract
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.Keywords
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