Abstract Algebra Cheat Sheet

This document provides definitions and propositions related to abstract algebra. It begins by defining a group as a set with a binary operation that is closed, associative, has an identity element, and where each element has an inverse. It then lists several propositions about properties of groups, including that a group has a unique identity and each element has a unique inverse. The document continues defining additional algebraic structures like rings, fields, subgroups, and properties of groups like cyclic groups. It concludes by discussing matrix groups and their properties.