Annali di Matematica Pura ed Applicata

, Volume 114, Issue 1, pp 173–194 | Cite as

Partitions and their stabilizers for line complexes and quadrics

  • R. H. Dye
Article

Summary

It is shown that PG(2Nr −1, q) can be partitioned by totally isotropic PG(r −1, q) of a non-singular line complex. The stabilizer in PSp2Nr(q) of the spread given is identified, and its geometric action is discussed. Using this partition and the various inter-relations of quadrics, line complexes and their groups when q is even we obtain various orbits of partitions of quadrics over GF(2α) by their maximal totally singular subspaces; the corresponding stabilizers in the relevant orthogonal groups are investigated. It is explained how some of these partitions naturally generalize Conwell's heptagons for the Klein quadric in PG(5, 2).

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1977

Authors and Affiliations

  • R. H. Dye
    • 1
  1. 1.Newcastle upon TyneEngland

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