When 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.
Thanks for pointing out the article. Simplifying previous results is not often rewarded professionally, but is greatly appreciated.
Another thank you for pointing to this article.
Just curious, but who is the author of this great blog? You should make yourself known.
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.