Journal of Statistical Theory and Practice

, Volume 6, Issue 1, pp 97–128 | Cite as

Steiner Quadruple Systems With Point-Regular Abelian Automorphism Groups

  • Akihiro Munemasa
  • Masanori SawaEmail author


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).

05E20 05B05 


Combinatorial design Graph Finite group Steiner system 


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Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Graduate School of Information SciencesNagoya UniversityNagoyaJapan

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