Steiner quadruple systems with point-regular abelian automorphism groups

Akihiro Munemasa, Masanori Sawa

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)97-128
Number of pages32
JournalJournal of Statistical Theory and Practice
Volume6
Issue number1
DOIs
Publication statusPublished - 2012 Mar 1

Keywords

  • Combinatorial design
  • Finite group
  • Graph
  • Steiner system

ASJC Scopus subject areas

  • Statistics and Probability

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