More balanced incomplete block designs from Frobenius groups
The author produces 2-(v,k,k) designs (i.e. 2-designs with \(\lambda =k)\) from Frobenius groups satisfying certain conditions, namely: (1) For nonzero a in N (the kernel of the group written additively) \(a^ K\) is disjoint from \((-a)^ K\), K being the complement; (2) For a in N, a not 0, \(\{\) \(a\}\cup a^ K\cup (-a)^ K\) is not a subgroup of N; (3) For each g in K the map \(a\mapsto a+a^ g\) is a bijection of N, where we write \(x^ g\) for the effect of acting on x by g. One takes as basic blocks the sets of condition (2) and ''translates'' them under N to get the design. The author gives non-Abelian examples: a 2- (15625,7,7) and a 2-(45619,39,39) among others.
scientific article; zbMATH DE number 3999939