Embedding a non-embeddable stable plane

Abstract

AaSTRACT. In [4], K. Strambach describes a 2-dimensional stable plane NaN admitting E = SL2R as a group of automorphisms such that there exists no E-equivarient embedding into a 2dimensional projective plane. R. LOwen [3] has given a 4-dimensional analogue NaC, admitting A = SL2C. He posed the question whether there are embeddings of Strambach's plane bar into NaC- We show that such embeddings exist, in fact we determine all £-equivariant embeddings of 2-dimensional stable planes admitting £ as a transitive group of automorphisms. 1. THE PLANES In the original definitions, the point space is taken to be N2 or C 2, respectively, and the lines are described as subsets of the point space. We wish to describe the resulting geometries by the method given in I-6]. Since this method applie~ only to point homogeneous geometries, we have to delete the origin. (1.1) NOTATION. We write