Multiplied configurations, series induced by correlations (Q867483)

The authors present a method for constructing configurations \(M^*\) by multiplying self-dual linear spaces \(M\). The operation of multiplication is defined by using a fixed involutory correlation. The structure of such geometries are studied. For example, it is investigated under which conditions \(M^*\) is Pappian or Desarguesian if the starting linear space \(M\) is Pappian or Desarguesian, respectively. The automorphism group of \(M^*\) is characterized in terms of the automorphism group of \(M\). The paper ends with an in-depth study of \(M^*\) in case where \(M\) is one of the Fano, the Desargues or the Pappus configuration.