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, q t) and for each of these sizes (and groups) we determine the exact number of point orbits of this size.
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References
T. Beth, D. Jungnickel and H. Lenz, Design Theory, Cambridge University Press, Cambridge (1986).
J. W. P. Hirschfeld, Projective Geometries over Finite Fields, Oxford University Press, Oxford (1979).
J. H. van Lint and R. M. Wilson, A Course in Combinatorics, Cambridge University Press, Cambridge (1992).
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Brown, J.M.N. 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, q t). Designs, Codes and Cryptography 32, 45–50 (2004). https://doi.org/10.1023/B:DESI.0000029211.79206.e1
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DOI: https://doi.org/10.1023/B:DESI.0000029211.79206.e1