Periodic Linear Transformations of Affine and Projective Geometries
- 1 January 1950
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 2, 149-151
- https://doi.org/10.4153/cjm-1950-013-9
Abstract
Introduction. In a paper called “A Theorem in Finite Projective Geometry and some Applications to Number Theory” [Trans. Amer. Math. Soc, vol. 43 (1938), 377-385], J. Singer proved that the finite projective geometry PG(s — 1,pn), that is the projective geometry of dimension s — 1 whose coordinate field is the Galois field GF(pn), admits a collineation L of period q = (psn — 1)/ (pn — 1). Since this q is the number of points of PG(s — 1, pn), Singer's result states that the points of PG(s — 1, pn) are cyclically arranged. Singer's construction of L uses the notion of a “primitive irreducible polynomial of degree 5 belonging to a field GF(pn) which defines a PG(s — 1, pn).”Keywords
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