| Revision as of 15:51, 25 February 2002 editZundark (talk | contribs)Extended confirmed users, File movers, Pending changes reviewers29,653 edits moved some talk here← Previous edit | Revision as of 20:19, 3 April 2002 edit undoToby~enwiki (talk | contribs)140 editsNo edit summaryNext edit → | ||
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| :Do you realise how complicated this is, especially for order 32? Doing order <= 15 might be feasible, however. --], 2002 Feb 22 | :Do you realise how complicated this is, especially for order 32? Doing order <= 15 might be feasible, however. --], 2002 Feb 22 | ||
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| It simply is not true that the translation group is "our first example of a ]" (as the article is currently arranged). (<b>Z</b>,+) is also a Lie group, it is simply ''discrete'', or 0 dimensional. 0 dimensional Lie groups are studied in ordinary group theory rather than Lie theory but they are still technically Lie groups. Hence the adjective "nondiscrete". -- ], 2002/04/03 | |||
Revision as of 20:19, 3 April 2002
We currently have two different group pages: Mathematical group and Mathematical Group. I suggest simply deleting Mathematical group and redirecting it to Mathematical Group.
- Seconded, with one caveat: the title of the final article should be "Mathematical group" to comply with naming standards. --AxelBoldt
Done.
Zundark, 2001-08-11
The axiom of closure:
(Closure) for all a and b in G, a * b belong to G.
is superfluous, by definition of a binary operation. It's worth mentioning that closure follows from the definition, though.
The test of closure in the examples is in fact a test that the described mapping is inded a binary operation.
Any thoughts before I wade on in and make changes?
"This was our first example of a non-abelian group, because the operation o here is not commutative as the table shows. " If the table did show commutativity, would it be symmetrical about the diagonal from top left to bottom right? TimJ 5 Feb 2002
- Yes. The group is abelian if and only if the table is symmetric about the main diagonal. --Zundark, 2002 Feb 5
Could someone put up a good description of Sylow's Theorem?
- See Sylow theorems.
Also, it'd be nice to see a page dedicated to examples of groups.
Nice exercise: Classify all (isomorphism classes of) groups of order <=60. I'd like to see a page on that.
- Do you realise how complicated this is, especially for order 32? Doing order <= 15 might be feasible, however. --Zundark, 2002 Feb 22
It simply is not true that the translation group is "our first example of a Lie group" (as the article is currently arranged). (Z,+) is also a Lie group, it is simply discrete, or 0 dimensional. 0 dimensional Lie groups are studied in ordinary group theory rather than Lie theory but they are still technically Lie groups. Hence the adjective "nondiscrete". -- Toby, 2002/04/03