\(t\)-divisible designs from imprimitive permutation groups
A \(t\)-divisible design \((t\)-DD) is known as a group divisible design if \(t=2\) and the size of a point class exceeds 1, and a \(t\)-DD is simply a \(t\)-design if a point class is of size 1. The author constructs \(t\)-DD's by means of \(R\)-permutation groups \((G,X,R)\), where \(R\) is an equivalence relation on the set \(X\) and \(G\) is an \(R\)-admissable permutation group on \(X\) that is \(t\)-\(R\)-transitive. He also introduces the idea of a transitive extension of such a group and links it with the extension of a \(t\)-DD. The 2-DD's and 3-DD's obtained by extensions of certain classical groups are classified as well.
scientific article; zbMATH DE number 94943