Groups with maximal irredundant covers and minimal blocking sets

Details Groups with maximal irredundant covers and minimal blocking sets Groups with maximal irredundant covers and minimal blocking sets

2009-01-13

arxiv.org/abs/0901.1793v1

Mathematics

Group Theory

to appear in Ars Combinatoria

Scientific paper

Let $n$ be a positive integer. Denote by $\mathrm{PG}(n,q)$ the $n$-dimensional projective space over the finite field $\mathbb{F}_q$ of order $q$. A blocking set in $\mathrm{PG}(n,q)$ is a set of points that has non-empty intersection with every hyperplane of $\mathrm{PG}(n,q)$. A blocking set is called minimal if none of its proper subsets are blocking sets. In this note we prove that if $\mathrm{PG}(n_i,q)$ contains a minimal blocking set of size $k_i$ for $i\in\{1,2\}$, then $\mathrm{PG}(n_1+n_2+1,q)$ 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.

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