Resolvable \(t\)-designs
Resolvable \(t\)-\((v=p^f+1,k,\lambda)\) designs are constructed where \(k\) is a divisor of \(v\) and \(p\) is a prime. The constructed designs admit the (large) automorphism groups PGL\((2,p^f)\) or PSL\((2,p^f)\), which we denote by \(G\). The main idea is to consider subgroups \(G > H > U\) so that \(U\) is the stabilizer of a block and the orbit of that block under \(H\) forms a partition of the point set (that is, a parallel class). In this manner, utilizing various group-theoretical results, many new infinite families of resolvable \(3\)-\((v,k,\lambda)\) designs are obtained that are block transitive under PGL\((2,p^f)\) or PSL\((2,p^f)\).
scientific article; zbMATH DE number 2091523