Transitive and Co–Transitive caps
نویسنده
چکیده
Let PG(r, q) be the projective space of dimension r over GF (q). A k–cap K̄ in PG(r, q) is a set of k points, no three of which are collinear [10], and a k–cap is said to be complete if it is maximal with respect to set–theoretic inclusion. The maximum value of k for which there is known to exist a k–cap in PG(r, q) is denoted by m2(r, q). Some known bounds for m2(r, q) are given below. Suppose that K̄ is a cap in PG(r, q) with automorphism group Ḡ0 ≤ PΓL(r + 1, q). Then K̄ is said to be transitive if Ḡ0 acts transitively on K̄, and co-transitive if Ḡ0 acts transitively on PG(r, q)− K̄. Our main result is the following theorem.
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