Groupprops:Groupprops versus Wikipedia

This is an article comparing the Groupprops wiki against:Wikipedia

In what ways do Groupprops and Wikipedia differ as tools for learning and reference in group theory? There are a number of important differences. To illustrate some of tese, we take a few example articles in Groupprops and Wikipedia.

Group

Compare: group (on groupprops) against group (on Wikipedia)

Content and style

The Groupprops articles on group starts off by putting the term group in its context" a basic definition in group theory. Then, without any intrudction, it gives a quick overview of the history of the term group, and then proceeds into the definition. Notice that the definition is given in subsections, in a relatively standardized format.

Next, there are sections on Examples, Properties, Constructions and Variations. Notice that the style is not too conversational, it is not intended to expostulate, rather, it is intended to store and to present links to other areas within group theory.

This content and style is designed keeping in mind tat the person coming to read this article is interested mainly in knowing the definition of group within the mathematical context and is not interested in an exposition on the subject.

The Wikipedia article on Group is aimed at a different audience. Since Wikipedia is a universal encyclopaedia, the introduction has to provide enough context for a person who may be coming from anywhere, following any link, to what a group is and where it stands in the universe. Thus, there are two introductory paragraphs that describe what kind of thing a group is. The style is more conversational and informal.

Notice also that this page is much more detailed, with every example of a group described in detail, rather than tersely stated. The idea is that a person reading te article should geta wholesome flavour of what a group is, even if that person is not too interested/involved in groups. The idea of Groupprops, on the other hand, is to act as a terse source of information, linking to all the relevant pages.

Edit history

The Wikipedia article on group theory has a long history of edits -- it has seen over 300 edits over more than four years. In contrast, the Groupprops article on a group is a one-person effort, and even if Groupprops takes off to a larger scale, is unlikely to be edited by more than a few dozen people.

A good flavour of the many issues that have been discussed while editing the Wikipedia page can be had from the talk page.

Normal subgroup

Compare normal subgroup (on groupprops) with normal subgroup (on Wikipedia)

Unlike group, the Wikipedia article on normal subgroup is considerably shorter than the Groupprops article. That is because while in the case of group, Wikipedia combined the definition part with a lot of historical motivation and a kind of basic group theory tutorial, in the normal subgroup case, it just provides the definition.

Notice here that the Groupprops article is much more structured, with clear parts related to History, Definition, Importance, Formalisms, Relation with other properties, Metaproperties and Testing. However, while more structured, this is also less friendly to people who just happen to be passing by the page, and is definitely more intimidating to people who are wondering whether to edit or alter it. That is because it uses a whole lot of conventions, templates etc. which are not adequately explained here. This again highlights the fact that Groupprops is intended for people with greater focus and a clear intention of getting the group theory contents.

Note that Groupprops does have survey and expostulatory articles, but these are typically kept separate from the main definition pages. For instance, Category:Survey articles related to normality has a list of survey articles (some of them incomplete at te timie of this writing) related to the subgroup property of normality.

The differences and why they exist

The main thing to remember about Groupprops is that it is not intended for merging into bigger encyclopaedias like Wikipedia, because that would cause its structure to get diluted and compromised. At best, we can hope that it will become part of a network of inter-related wikis on topics related to mathematics, where one can easily go from one to the other.

Similarly, Wikipedia would not benefit, and probably would not be able to sustain, a format specially suited for group theory articles. It is able to impose global guidelines on the structure of articles, though these again take time ot propagate. However, it cannot make special formats suited for group theory articles since these may go head-on against whatever are the globally suited formats, and besides, there is no clear borederline between group theory and non-group theory articles.

Also, it is my belief that we need (or would benefit from) wikis of all sorts -- some which are focussed and structured in the Groupprops-fashion, some which are more broad-based and can be integrated into other frameworks, some of the Wikipedia kind, some in between. The idea is that each person can understand things in whatever way suits him/her best for that local context.