# Accession Number:

## AD0698301

# Title:

## AFFINE GENERALIZED QUADRILATERALS,

# Descriptive Note:

# Corporate Author:

## CALIFORNIA INST OF TECH PASADENA

# Personal Author(s):

# Report Date:

## 1969-01-01

# Pagination or Media Count:

## 8.0

# 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 i1, i 0, ..., m - 1. The chain is irreducible if e sub i does not equal e sub i2 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:

# Subject Categories:

- Theoretical Mathematics