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$\mathbb{P}(q)$-Groupoids of Conway Type

Veronica Kelsey, Peter Rowley

Abstract

In the spirit of Conway we define a groupoid starting from projective planes of order $q$, where $q$ is odd. The associated group of these groupoids is then investigated.

$\mathbb{P}(q)$-Groupoids of Conway Type

Abstract

In the spirit of Conway we define a groupoid starting from projective planes of order , where is odd. The associated group of these groupoids is then investigated.

Paper Structure

This paper contains 3 sections, 5 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of Theorem \ref{['main']}

Key Result

Theorem 1

Let $q>3$ be an odd prime power, $\alpha$ a fixed point of $\mathcal{P}(q)$ and set $\Omega = \mathcal{P}(q) \backslash \{\alpha\}$. Then

Theorems & Definitions (11)

  • Theorem 1
  • Lemma 2.1
  • proof
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Remark 3.3
  • Lemma 3.4
  • proof
  • ...and 1 more