Tour:Getting started (beginners)
We are about to get started on the guided tour for beginners. To get the most from this guided tour, stay faithful to it, i.e. read the articles in the order suggested. You will have various opportunities for detours: some other articles to read so as to get a better understanding of what you're touring, and some just for entertainment. Please try to open these detours in different windows/tabs so that you do not lose track of where you are in the main tour.
This tour is not intended to be a complete introduction to group theory, or a replacement for textbook or course materials. Rather, it is intended as a supplement. To get the most from this tour, keep open your main course book or lecture notes and make sure you can map what's there on the wiki, with what you're learning in the course or from the textbook.
The tour is structured as follows.
Get started with Guided tour for beginners:Introduction one
This part provides some very basic, introductory definitions. We do not focus here on the example-oriented motivation for these definitions. The definitions provided are:
Prerequisites for this part:
- An understanding of set-theoretic notation
- A basic understanding of functions between sets, unary and binary operations, and relations
The goal of this part is to:
- Provide a basic understanding of the definitions of group, subgroup, trivial group, and Abelian group
Get started with Guided tour for beginners:Introduction two
This part focuses on providing an understanding of how to do simple manipulations involving groups. We begin by generalizing some of the ideas involving groups, and discussing proofs involving some of the basic manipulations.
Prerequisites: Part one (or equivalent)
The goal of this part is to give comfort in simple manipulations involving groups.
Articles covered in this part are:
- Some variations of group
- Equality of left and right neutral element
- Equality of left and right inverses
- Equivalence of definitions of group
- Invertible implies cancellative
- Associative binary operation
- Finite group
- Subsemigroup of finite group is subgroup
- Sufficiency of subgroup criterion
- Manipulating equations in groups
Continue to the definition of a group