Classification of finite 3-nets of types I.3, I.4, I.5

Abstract

Using the description of 2-transitive groups, in this paper finite 3-nets of types I.3, I.4, and I.5 are studied. According to the Barlotti-Strambach classification (see [4]) an arbitrary 3-net belongs to one of the seven Lent classes I.1-I.5, II.1-II.2. In this work the question of the existence of nets of types 1.3, 1.4, 1.5 remained open. The non-existence of a finite net of type 1.5 is proved and the finite nets of type 1.3 and 1.4 are described up to isomorphism.