On Homomorphisms of Projectile Planes.
Abstract
In the study one has defined a homomorphism between two projective planes mapping a line into finitely many collinear points. This homomorphism induces a homomorphism between their ternary rings. Using the ternary ring homomorphism it has been shown that the homomorphism between two planes preserves properties like those of being a Bol plane, a translation plane, a Moufang plane or a Desarguesian plane. Next it has been shown that new homomorphisms can be constructed from the old homomorphism. Also it has been shown that under certain conditions collineations in one plane induce collineations in the second plane. One has then considered planes coordinatized by non-alternative division rings. In this case it has been shown that the elementary group of the first plane has a subgroup inducing the elementary group of the second plane. Lastly, the author has obtained conditions under which the homomorphic image of a plane may be a translation plane, a Moufang plane or a Desarguesian plane even though the original plane may not be so. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1970
- Accession Number
- AD0714171
Entities
People
- Bepin B. Mehra
Organizations
- University of Iowa