Talk:Finite group
 | This article is rated C-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
| |||||||||||
Errr ... shouldn't this page have some content ...
Charles Matthews 14:46, 4 May 2004 (UTC)
OK ( three years later): The section on number of groups with a given set was incorrect, so I have replaced it. Messagetolove 01:22, 13 May 2007 (UTC)
A table of how many distinct groups for each order[edit]
There are textbooks and other references that present tables of how many distinct (non-isomorphic) groups exist for each order, for a reasonable range of integers such as n = 1, 2, 3, ... 30. Such a thing here would be a valuable example of concrete information, rather than abstrct wandering around (wondering around?) about the subject. Such a table should be provided here.
For example with n = 8, there is the cyclic abelian group that can be illustated as the one that consists of the eight eighth=roots of -1. Also, there is the quaternion group (with n = 8, I emphasize) that is a non-abelian group. A non-abelian group cannot possibly be isomorphic to an abelian group, hence for n = 8, there are at least two distinct groups in existence.
Upon further investigation, it is found that there are three abelian groups here, including two product groups plus two non-abelian groups, with order eight.
98.81.17.64 (talk) 22:32, 4 August 2010 (UTC)
- You may be looking for the page list of small groups. It doesn't construct the enumeration like you describe (Wikipedia is not a textbook), but it does enumerate exhaustively all groups up to and including order 16. Baccyak4H (Yak!) 14:19, 5 August 2010 (UTC)
- I don't see any utility in listing the numbers of isomorphism classes of groups of small order, especially since the groups themselves have been listed elsewhere. Arcfrk (talk) 15:49, 5 August 2010 (UTC)
Another three years later[edit]
To echo the comments of Charles Matthews from 2004 and the follow-up in 2007, finite group theory is a well established subject. Focusing entirely on the number of finite groups of given order is misleading. Arcfrk (talk) 15:56, 5 August 2010 (UTC)
Request for Rewrite[edit]
This article is way too small, and doesn't talk at all about permutation groups, cyclic groups, etc. Instead it rants on about the the number of groups with n elements. The introduction is fine, but after that there is virtually no good information shown. Fraqtive42 (talk) 04:07, 14 September 2011 (UTC)