On Pappus Configurations in Hall Planes

TL;DR

This paper investigates Pappus configurations within finite Hall planes, which are non-Desarguesian, and establishes weaker versions of Pappus's Theorem applicable to these planes.

Contribution

It introduces and proves weaker forms of Pappus's Theorem tailored for Hall planes, expanding understanding of geometric properties in non-Desarguesian finite planes.

Findings

Weaker Pappus configurations are valid in Hall planes.

Certain classical geometric theorems do not fully hold in Hall planes.

New variants of Pappus's Theorem are established for Hall planes.

Abstract

As the finite Hall planes are Non-Desarguesian, the Pappus Theorem does not hold in them. In this paper we state and prove some weaker versions of Pappus's Theorem in Hall planes.