Minimal Blocking Sets inPG(n, 2) and Covering Groups by Subgroups
| Autor: | M. J. Ataei, Alireza Abdollahi, A. Mohammadi Hassanabadi |
|---|---|
| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Communications in Algebra. 36:365-380 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927870701715639 |
| Popis: | In this article we prove that a set of points B of PG(n, 2) is a minimal blocking set if and only if ⟨B⟩ = PG(d, 2) with d odd and B is a set of d + 2 points of PG(d, 2) no d + 1 of them in the same hyperplane. As a corollary to the latter result we show that if G is a finite 2-group and n is a positive integer, then G admits a ℭ n+1-cover if and only if n is even and G≅ (C 2) n , where by a ℭ m -cover for a group H we mean a set 𝒞 of size m of maximal subgroups of H whose set-theoretic union is the whole H and no proper subset of 𝒞 has the latter property and the intersection of the maximal subgroups is core-free. Also for all n 0 an integer and p a prime number) for which there is a blocking set B of size n in PG(m,p) such that ⟨B⟩ = PG(m,p). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|