On the Action of the Groups GL(n+1, q), PGL(n + 1, q), SL(n + 1, q) and PSL(n + 1, q) on PG(n, qt)

  • Authors:

  • Julia M. N. Brown

  • Affiliations:

  • Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada juliamnb@yorku.ca

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2004

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Abstract

Let q be a prime power and let n ≥ 0, t ≥ 1 be integers. We determine the sizes of the point orbits of each of the groups GL(n + 1, q), PGL(n + 1, q), SL(n + 1, q) and PSL(n + 1, q) acting on PG(n, qt) and for each of these sizes (and groups) we determine the exact number of point orbits of this size.