## Abstract

In this article we present a graph theoretic construction of Steiner quadruple systems (SQS) admitting Abelian groups as point-regular automorphism groups. The resulting SQS has an extra property that we call A-reversibility, where A is the underlying Abelian group. In particular, when A is a 2-group of exponent at most 4, it is shown that an A-reversible SQS always exists. When the Sylow 2-subgroup of A is cyclic, we give a necessary and sufficient condition for the existence of an A-reversible SQS, which is a generalization of a necessary and sufficient condition for the existence of a dihedral SQS by Piotrowski (1985). This enables one to construct A-reversible SQS for any Abelian group A of order v such that for every prime divisor p of v there exists a dihedral SQS(2p).

Original language | English |
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Pages (from-to) | 97-128 |

Number of pages | 32 |

Journal | Journal of Statistical Theory and Practice |

Volume | 6 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Mar 1 |

## Keywords

- Combinatorial design
- Finite group
- Graph
- Steiner system

## ASJC Scopus subject areas

- Statistics and Probability