Simple abelian quadruple systems

Abstract

We generalize a construction of simple cyclic 3-designs due to Köhler (1981) to that of simple abelian 3-designs. We prove that for any abelian group A of order $v\equiv 2(\mathrm{mod}4)$, there exists a simple 3-$(v,4,3)$ design with $A⋊\mathrm{Aut}(A)$ as an automorphism group.