|WikiProject Mathematics||(Rated C-class, High-importance)|
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
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. 126.96.36.199 (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
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
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)