Steiner quadruple systems with point-regular abelian automorphism groups

Details Steiner quadruple systems with point-regular abelian automorphism groups Steiner quadruple systems with point-regular abelian automorphism groups

2009-10-15

arxiv.org/abs/0910.2759v4

Mathematics

Combinatorics

31 pages

Scientific paper

In this paper 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 which 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).

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