Accession Number : AD0714171

Title :   On Homomorphisms of Projectile Planes.

Descriptive Note : Technical rept.,

Corporate Author : IOWA UNIV IOWA CITY DEPT OF MATHEMATICS

Personal Author(s) : Mehra,Bepin B.

Report Date : JUL 1970

Pagination or Media Count : 59

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)

Descriptors :   (*PROJECTIVE GEOMETRY, GROUPS(MATHEMATICS)), (*ALGEBRAS, RINGS(MATHEMATICS)), MAPPING(TRANSFORMATIONS), SET THEORY, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE