### Some Additive $2-(v,5,\lambda )$ Designs

Andrea Caggegi (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Given a finite additive abelian group $G$ and an integer $k$, with $3\le k\le \left|G\right|$, denote by ${\mathcal{D}}_{k}\left(G\right)$ the simple incidence structure whose point-set is $G$ and whose blocks are the $k$-subsets $C=\{{c}_{1},{c}_{2},\cdots ,{c}_{k}\}$ of $G$ such that ${c}_{1}+{c}_{2}+\cdots +{c}_{k}=0$. It is known (see [Caggegi, A., Di Bartolo, A., Falcone, G.: Boolean 2-designs and the embedding of a 2-design in a group arxiv 0806.3433v2, (2008), 1–8.]) that ${\mathcal{D}}_{k}\left(G\right)$ is a 2-design, if $G$ is an elementary abelian $p$-group with $p$ a prime divisor of $k$. From [Caggegi, A., Falcone, G., Pavone, M.: On the additivity...