Groups of Order Sixteen
April 8th, 2008 by WaltWhen I first took abstract algebra, I loved theorems classifying all of the groups of a certain order. Here is a paper I would have loved, The Groups of Order Sixteen Made Easy. Normally, the classification of groups of order 16 is described in terms of group extensions and the theory of p groups. The author bypasses all that to give a more elementary derivation.
Via God Plays Dice.
April 9th, 2008 at 3:18 am
Thanks for pointing out the article. Simplifying previous results is not often rewarded professionally, but is greatly appreciated.
April 12th, 2008 at 3:36 am
Another thank you for pointing to this article.
April 15th, 2008 at 2:55 pm
Just curious, but who is the author of this great blog? You should make yourself known.
April 16th, 2008 at 3:15 pm
A few links into the references on this post turned up an unfamiliar way of appreciating the rarity of non-solvable groups:
If you call a number “solvable” if every group of that order is solvable, then…
A positive integer n is a non-solvable number if and only if it is a multiple of any of the following numbers: a) 2^p(2^2p-1), p any prime. b) 3^p(3^2p-1)/2, p odd prime. c) p(p^2-1)/2, p prime greater than 3 such that p^2+1 = 0 (mod 5). d) 2^4*3^3*13. e) 2^2p(2^2p+1)(2^p-1), p odd prime.