AFFINE GENERALIZED QUADRILATERALS,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1969
- Accession Number
- AD0698301
Entities
People
- Marshall Hall Jr.
Organizations
- California Institute of Technology