Groups with maximal irredundant covers and minimal blocking sets

Abstract

Let n be a positive integer. Denote by PG(n,q) the n-dimensional projective space over the finite field Fq, of order q. A blocking set in PG(n,q) is a set of points that has non-empty intersection with every hyperplane of PG(n,q). A blocking set is called minimal if none of its proper subsets are blocking sets. In this note we prove that if PG(n,q) contains a minimal blocking set of size κi for i ∈ {1,2}, then PG(n1 + n2 + 1,q) contains a minimal blocking set of size κ1+κ2 - 1. This result is proved by a result on groups with maximal irredundant covers.