Accession Number : AD0698301

Title :   AFFINE GENERALIZED QUADRILATERALS,

Corporate Author : CALIFORNIA INST OF TECH PASADENA

Personal Author(s) : Hall,Marshall , Jr

Report Date : 1969

Pagination or Media Count : 8

Abstract : Feit and Higman have defined a generalized n-gon as a system N of points and lines together with incidences of certain points on certain lines such that each line contains 1 + s points and each point in on 1 + t lines. Furthermore a chain of length m, e = e sub 0, e sub 1, ..., e sub m = f is a sequence in which e sub i is incident with e sub (i+1), i = 0, ..., m - 1. The chain is irreducible if e sub i does not equal e sub (i+2) i = 0,..., m - 2. We put lambda (e, f) = m if this is the shortest chain joining e and f. We call a chain closed if e sub m = e sub 0. Then N is a generalized n-gon if lambda (e, f) = or < n for every e and f of N and if N does not contain a closed irreducible chain of length 2m with M < n. In this paper a construction is given for generalized quadrilaterals (4-gons above) with s = q - 1, t = q + 1 where q = 1 to the power e, e = or > 2. (Author)

Descriptors :   (*GEOMETRY, THEOREMS), PROJECTIVE GEOMETRY, GROUPS(MATHEMATICS), GRAPHICS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE