Minimal blocking sets in PG(n,2) and covering groups by subgroups
| dc.creator | Abdollahi, Alireza | |
| dc.creator | Ataei, M. J. | |
| dc.creator | Hassanabadi, A. Mohammadi | |
| dc.date | 2007-08-16 | |
| dc.date.accessioned | 2026-07-07T08:24:02Z | |
| dc.date.available | 2026-07-07T08:24:02Z | |
| dc.description | In this paper 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 $\mathfrak{C}_{n+1}$-cover if and only if $n$ is even and $G\cong (C_2)^{n}$, where by a $\mathfrak{C}_m$-cover for a group $H$ we mean a set $\mathcal{C}$ of size $m$ of maximal subgroups of $H$ whose set-theoretic union is the whole $H$ and no proper subset of $\mathcal{C}$ has the latter property and the intersection of the maximal subgroups is core-free. Also for all $n<10$ we find all pairs $(m,p)$ ($m>0$ an integer and $p$ a prime number) for which there is a blocking set $B$ of size $n$ in $PG(m,p)$ such that $<B>=PG(m,p)$. | |
| dc.identifier | https://arxiv.org/abs/0708.2282 | |
| dc.identifier | http://arxiv.org/abs/0708.2282 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136210 | |
| dc.subject | Group Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 51E21, 20D60 | |
| dc.title | Minimal blocking sets in PG(n,2) and covering groups by subgroups | |
| dc.type | text |