On the minimum number of points covered by a set of lines in $$PG(2, q)$$PG(2,q)

The classification of the 2-designs with λ = 2 admitting a flag-transitive automorphism groups with socle P S L ( 2 , q ) is completed by settling the two open cases in [2]. The result is achieved by using conics and hyperovals of P G ( 2 , q ).

Consider two symmetric $$3 \times 3$$3 3 matrices $$A$$A and $$B$$B with entries in $$GF(q)$$GF(q), for $$q=p^n$$q=pn, $$p$$p an odd prime. The zero sets of $$v^T Av$$vTAv and $$v^T Bv$$vTBv, for $$v \in GF(q)^3$$v GF(q)3 and $$v\ne 0$$v 0, can be ...

For an odd prime p 7, let q be a power of p such that $${q^3\equiv1 \pmod 7}$$ . It is known that the desarguesian projective plane PG (2, q ) of order q has a unique conjugacy class of projectivity groups isomorphic to PSL (2, 7). For such a projective group Γ, we ...