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

From Groupprops
Jump to: navigation, search
(Part two)
Line 69: Line 69:
 
* [[Guided tour for beginners:Join of subgroups|Join of subgroups]]
 
* [[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]]
 
* [[Guided tour for beginners:Some examples of groups and subgroups|Some examples of groups and subgroups]]
 +
 +
==Part four==
 +
 +
''Not yet prepared''
 +
 +
* [[Guided tour for beginners:Homomorphism of groups|Homomorphism of groups]]
 +
* [[Guided tour for beginners:Isomorphism of groups|Isomorphism of groups]]
 +
* [[Guided tour for beginners:Isomorphic groups|Isomorphic groups]]
 +
* [[Guided tour for beginners:Endomorphism of a group|Endomorphism of a group]]
 +
* [[Guided tour for beginners:Automorphism of a group|Automorphism of a group]]
 +
* [[Guided tour for beginners:Automorphism group|Automorphism group]]
 +
* [[Guided tour for beginners:Inner automorphism|Inner automorphism]]
 +
* [[Guided tour for beginners:Kernel|Kernel]]
 +
* [[Guided tour for beginners:Normal subgroup|Normal subgroup]]
 +
* [[Guided tour for beginners:Quotient group|Quotient group]]
 +
* [[Guided tour for beginners:First isomorphism theorem|First isomorphism theorem]]
 +
* [[Guided tour for beginners:Second isomorphism theorem|Second isomorphism theorem]]
 +
* [[Guided tour for beginners:Third isomorphism theorem|Third isomorphism theorem]]
 +
 +
==Part five==
 +
 +
* [[Guided tour for beginners:Characteristic subgroup|Characteristic subgroup]]
 +
* [[Guided tour for beginners:Characteristic implies normal|Characteristic implies normal]]
 +
* [[Guided tour for beginners:External direct product|External direct product]]
 +
* [[Guided tour for beginners:Internal direct product|Internal direct product]]
 +
* [[Guided tour for beginners:Group property|Group property]]
 +
* [[Guided tour for beginners:Subgroup property|Subgroup property]]
 +
* [[Guided tour for beginners:Subgroup-defining function|Subgroup-defining function]]
 +
* [[Guided tour for beginners:Center|Center]]
 +
* [[Guided tour for beginners:Characteristic of normal implies normal|Characteristic of normal implies normal]]
 +
* [[Guided tour for beginners:Commutator subgroup|Commutator subgroup]]
 +
* [[Guided tour for beginners:Normality is strongly intersection-closed|Normality is strongly intersection-closed]]
 +
* [[Guided tour for beginners:Normality is strongly join-closed|Normality is strongly join-closed]]
 +
* [[Guided tour for beginners:Invariance property|Invariance property]]

Revision as of 23:34, 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:

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.

Part four

Not yet prepared

Part five