| Abstract: | Summary The theory of linear representations of projective planes developed by Bruck and one of the authors (Bose) in two earlier
papers J. Algebra1 (1964), pp. 85–102 and4 (1966), pp. 117–172] can be further extended by generalizing the concept of incidence adopted there. A linear representation is obtained for
a class of non-Desarguesian projective planes illustrating this concept of generalized incidence. It is shown that in the
finite case, the planes represented by the new construction are derived planes in the sense defined by Ostrom Trans. Amer.
Math Soc.111 (1964), pp. 1–18] and Albert Boletin Soc. Mat. Mex,11 (1966), pp, 1–13] of the dual of translation planes which can be represented in a 4-space by the Bose-Bruck construction. An analogous interpretation
is possible for the infinite case.
This research was sponsored by the National Science Foundation under Grant No. GP-8624, and the U.S. Air Force Office of Scientific
Research under Grant No. AFOSR-68-1406.
This research was conducted while the author was visiting professor at the University of North Carolina at Chapel Hill. His
research was also partially supported by C.N.R.
Entrata in Redazione il 28 maggio 1970. |
