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

Caggegi, Andrea. "Some Additive $2-(v, 5,\lambda )$ Designs." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 54.1 (2015): 65-80. <http://eudml.org/doc/271645>.

@article{Caggegi2015,
abstract = {Given a finite additive abelian group $G$ and an integer $k$, with $3\le k \le |G|$, denote by $\mathcal \{D\}_k (G)$ the simple incidence structure whose point-set is $G$ and whose blocks are the $k$-subsets $C = \lbrace c_1, c_2,\dots , c_k\rbrace $ of $G$ such that $c_1 + c_2+\dots +c_k = 0$. 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 $\mathcal \{D\}_k (G)$ 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 of block design submitted.] we know that $\mathcal \{D\}_3(G)$ is a 2-design if and only if $G$ is an elementary abelian 3-group. It is also known (see [Caggegi, A.: Some additive $2-(v,4,\lambda )$ designs Boll. Mat. Pura e Appl. 2 (2009), 1–3.]) that $G$ is necessarily an elementary abelian 2-group, if $\mathcal \{D\}_4(G)$ is a 2-design. Here we shall prove that $\mathcal \{D\}_5(G)$ is a 2-design if and only if $G$ is an elementary abelian 5-group.},
author = {Caggegi, Andrea},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Conformal mapping; geodesic mapping; conformal-geodesic mapping; initial conditions; (pseudo-) Riemannian space},
language = {eng},
number = {1},
pages = {65-80},
publisher = {Palacký University Olomouc},
title = {Some Additive $2-(v, 5,\lambda )$ Designs},
url = {http://eudml.org/doc/271645},
volume = {54},
year = {2015},
}

TY - JOUR
AU - Caggegi, Andrea
TI - Some Additive $2-(v, 5,\lambda )$ Designs
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2015
PB - Palacký University Olomouc
VL - 54
IS - 1
SP - 65
EP - 80
AB - Given a finite additive abelian group $G$ and an integer $k$, with $3\le k \le |G|$, denote by $\mathcal {D}_k (G)$ the simple incidence structure whose point-set is $G$ and whose blocks are the $k$-subsets $C = \lbrace c_1, c_2,\dots , c_k\rbrace $ of $G$ such that $c_1 + c_2+\dots +c_k = 0$. 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 $\mathcal {D}_k (G)$ 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 of block design submitted.] we know that $\mathcal {D}_3(G)$ is a 2-design if and only if $G$ is an elementary abelian 3-group. It is also known (see [Caggegi, A.: Some additive $2-(v,4,\lambda )$ designs Boll. Mat. Pura e Appl. 2 (2009), 1–3.]) that $G$ is necessarily an elementary abelian 2-group, if $\mathcal {D}_4(G)$ is a 2-design. Here we shall prove that $\mathcal {D}_5(G)$ is a 2-design if and only if $G$ is an elementary abelian 5-group.
LA - eng
KW - Conformal mapping; geodesic mapping; conformal-geodesic mapping; initial conditions; (pseudo-) Riemannian space
UR - http://eudml.org/doc/271645
ER -