Groups of order 8 and 16

TL;DR

This paper provides a simplified and clearer exposition of the classification of groups of order 16, inspired by a course and correcting previous typos and complexities in existing literature.

Contribution

It offers a simplified proof and presentation of the classification of groups of order 16, improving accessibility for students and researchers.

Findings

Simplified classification proof of groups of order 16

Clarified previous typos in existing literature

Enhanced understanding of p-group classification

Abstract

This document is rather a course about groups than a research paper. However, it can be of interest for many master students in mathematics which are devoted to the p-group classification theory. This paper is inspirated of the course of David Clausen from the university of Puget Sound (USA) on the classification of groups of order 16. His publication was made on GNU Licence. However, his publication contained some typo errors which make difficult the understanding of his method. Moreover, his proof, although interesting, is not the simplest. In my document, while keeping the development that he proposed, I greatly simplified his proof of classification of groups of order 16.