GROUPS WITH MAXIMAL IRREDUNDANT COVERS AND MINIMAL BLOCKING SETS

摘要

Let n be a positive integer. Denote by PG(n,q) the n-dimensional projective space over the finite field F_q 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_i,q) contains a minimal blocking set of size k_i for i ? {1,2}, then PG(n_1 + n_2 + 1,q) contains a minimal blocking set of size k_1+k_2-1. This result is proved by a result on groups with maximal irredundant covers.