Groupprops:Purpose statement

I begin by trying to bring out what the motivation behind groupprops is, why I think such an effort can be necessary and useful, and how we are going about it.

To read a more fiery description of our goals and what makes us special, check out Groupprops:What makes us special.

The purpose of groupprops
Groupprops is intended as an active repository of definitions, facts, proofs, and motivational material in the theory of groups, subgroups, automorphisms, and representations. Groupprops aims to be:


 * A quick reference tool for gathering the basic definition and important properties of any term/concept
 * A quick tool to check whether a particular fact (in group theory) is true, and to find facts related to a particular term
 * A quick tool to understand the proof of a result and figure out whether that proof is applicable in other contexts
 * A place where one can read articles motivating the development of any term or concept, as well as survey articles explaining the application of a principle or idea or related cluster of ideas

Who is this wiki for?
This wiki is intended to simultaneously serve the needs of a vast audience:


 * People just beginning or starting out in group theory may like to check Groupprops:Guided tour for beginners
 * People who have a grounding in group theory (upto a first course) may like to check Groupprops:Guided tour for semi-beginners
 * People who are interested in computational group theory
 * People who are interested in the theory of finite groups (such as the classification of finite simple groups)
 * People who are interested in linear representation theory of groups

I plan to prepare guided tours for each of the different target segments of this wiki.

Groupprops versus Wikipedia
Isn't Wikipedia the canonical place to post stuff on group theory? When an online repository of all the definitions and facts exist, why bother to have a different and separate wiki for group theory?

What is the advantage of having a wiki specifically catered to group theory?

The advantages are as follows:


 * Organizational flexibility: I initially started out by making edits on Wikipedia to include stuff in group theory. But I found that many of Wikipedia's edit policies, including those on categorization, original research, constrained the way I would like to organize the stuff in group theory.


 * The content of an individual article: The typical Wikipedia article is meant for a random person, and often reads like: "In the realm of mathematics, in algebra, in group theory, a subgroup of a group is ..." It is difficult to create one's own style sheet that demarcates the history of the term, the definition of the term, the properties, the stronger and weaker properties, the behavior under various operators. This is because a whole lot of people have widely varying views and there is an inertia that is hard to overcome.


 * The ability to separate fact articles and proof articles: Check out the upcoming Groupprops:Organizational principles for more.

There is, of course, a more general question: why have multiple wikis at all and why not have a single canonical wiki? I think this question is well-addressed at the Quantum theory wiki hosted by Caltech.

Groupprops versus more professional efforts
Another question I want to address is: how am I, as am amateur B.Sc. student, qualified to run a wiki on group ptheory, when I don't know too much of it? To answer this question, let me clarify that this is not the wiki on group theory -- it is just an effort in the direction of building a group theory wiki. If other wikis take off better, then those are the ones that will remain in history, and the groupprops wiki could just be one of the many wikis that lies rotting away.

It is also possible that a more successful wiki may still find useful things to borrow from groupprops.

Groupprops versus books and journal articles
How does groupprops, with its aim of providing complete proofs, compare with books and journal articles? Groupprops is definitely not a substitute for a journal paper, since it provides only a toned down and sanitized proof as opposed to a journal article that develops the problem fully in its own right and then outlines a proof or a solution.

However, what I think groupprops could be effectively used for is to get a quick idea of a proof without having to invest into entering the paper and all its notation. It can also be used for effective hopping between results based on various parameters (similarity of the statement, similarity of the proof).

Who runs the wiki?
Currently, the wiki is run by me, and I will soon be putting up policies for collaborative editing.

What are the expansion plans?
These will be described on Groupprops:Expansion plans.