André structure and S-spaces with translation. II (Q801292)

In a former work [Geom. Dedicata 10, 113-128 (1981; Zbl 0459.51002)], the author began to study a class of finite André-structures with parallelism, exactly the Sperner spaces with a translation group, which in general is not transitive. It is the purpose of this work to study in a detailed way the finite André-structures, with a translation group such that the stabilizer of a line is never identical. To this aim the author gives a group representation of such structures by means of the partitions of a finite group. In this way many results of various types are obtained; moreover two methods are given in order to construct new examples of such structures.