# Difference between revisions of "Tour:Getting started (beginners)"

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Continue to [[Guided tour for beginners:Group|the definition of a group]] | Continue to [[Guided tour for beginners:Group|the definition of a group]] | ||

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+ | ==Part three== | ||

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+ | {{quotation|Get started with [[Guided tour for beginners:Introduction three]]}} | ||

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+ | Prerequisites: Part two or equivalent | ||

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+ | This part focuses a bit more on subgroups; the notion of intersection and union of subgroups and whether a union of subgroups is a subgroup. | ||

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+ | * [[Guided tour for beginners:Intersection of subgroups is subgroup|Intersection of subgroups is subgroup]] | ||

+ | * [[Guided tour for beginners:Union of two subgroups is not a subgroup|Union of two subgroups is not a subgroup]] | ||

+ | * [[Guided tour for beginners:Left coset of a subgroup|Left coset of a subgroup]] | ||

+ | * [[Guided tour for beginners:Left cosets are in bijection via left multiplication|Left cosets are in bijection via left multiplication]] | ||

+ | * [[Guided tour for beginners:Right coset of a subgroup|Right coset of a subgroup]] | ||

+ | * [[Guided tour for beginners:Left and right coset spaces are naturally isomorphic|Left and right coset spaces are naturally isomorphic]] | ||

+ | * [[Guided tour for beginners:Lagrange's theorem|Lagrange's theorem]] | ||

+ | * [[Guided tour for beginners:Generating set of a group|Generating set of a group]] | ||

+ | * [[Guided tour for beginners:Subgroup generated by a subset|Subgroup generated by a subset]] | ||

+ | * [[Guided tour for beginners:Join of subgroups|Join of subgroups]] | ||

+ | * [[Guided tour for beginners:Some examples of groups and subgroups|Some examples of groups and subgroups]] |

## Revision as of 22:35, 22 March 2008

Get started

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.

## Part one

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

## Part two

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

## Part three

Get started with Guided tour for beginners:Introduction three

Prerequisites: Part two or equivalent

This part focuses a bit more on subgroups; the notion of intersection and union of subgroups and whether a union of subgroups is a subgroup.

- Intersection of subgroups is subgroup
- Union of two subgroups is not a subgroup
- Left coset of a subgroup
- Left cosets are in bijection via left multiplication
- Right coset of a subgroup
- Left and right coset spaces are naturally isomorphic
- Lagrange's theorem
- Generating set of a group
- Subgroup generated by a subset
- Join of subgroups
- Some examples of groups and subgroups