Tricki
a repository of mathematical know-how

Revision of Group theory front page from Sun, 05/04/2009 - 02:39

Quick description

This article contains links to pages about techniques that are specific to group theory.

Note iconIncomplete This article is incomplete. This article could do with some general discussion about different kinds of proofs in group theory, and more links to subsidiary pages, whether or not those pages have been written yet.
  • How to find groups with given properties Quick description. ( If you are trying to prove a statement about all groups with a certain property, then it helps to have a repertoire of examples and methods of construction, so that you can get a feel for whether the statement is true. This article is about various methods for building groups. )

    • Basic examples of groups Quick description. ( This article lists various important groups and families of groups, and discusses some of their properties. )

    • Presentations of groups Quick description. ( This article is about defining groups by means of generators and relations. )

  • How to use group actions Quick description. ( Many problems in group theory that do not explicitly mention group actions can be solved by means of a clever choice of action. This article gives some examples, and tips for choosing an appropriate action. )

Comments

Inline comments

The following comments were made inline in the article. You can click on 'view commented text' to see precisely where they were made.

Do we want these subarticles?

This page seems to me to be shaping up nicely, but I'd like to raise a question about all the dead links in these three paragraphs. The implication seems to be that there will be pages called "Abelian groups front page", "Finite groups front page", "Lie groups front page", "Profinite groups front page", "Combinatorial group theory front page" and "Geometric group theory front page". Is that the idea?

If it is (and it seems sensible), then at some stage I would probably want to rewrite this section slightly, in order to avoid the impression it currently gives that the Tricki focuses on subject matter (things like the definition of an Abelian group) rather than proof techniques. So I'd probably make those dead links into Wikipedia links and then have a paragraph saying something like "These special classes of groups have their own particular techniques, which are discussed and linked to from the following pages."

I suppose you're saying that

I suppose you're saying that you'd rather have pages with names like "How to solve a problem about finite groups", right? I'm all for that. I'll make the change at some point.

Yes. My first choice is

Yes. My first choice is titles like "To prove that a small group is simple, look at the sizes of the conjugacy classes," but that won't work for more general pages that discuss or link to several techniques. So then titles such as you suggest (perhaps I'd go for "problems" rather than "a problem" but that's a very minor quibble!) would come into play.

I updated the link to the How

I updated the link to the How to prove facts about finite groups by induction on the order page to take into account the new name of that page, and moved it so as to be under the How to solve problems about finite groups link.