Main Results

The Holder Program was a bold course to take. Classifying all possible simple groups was a heroic effort. It would seem that even tackling the problem of finding all possible simple groups between a certain range could be a daunting task. But using the preceding theorems and properties it is possible to eliminate many possible simple group orders contained in relatively large intervals with very little analysis. And although we are not including it in this paper, arguably the most powerful theorem was the Feit-Thompson paper proving that all groups of odd order are solvable. This is equivalent to the only simple groups of odd order being those of prime order. But even without this dramatic result, large progress can be made. In this case, we are concerned with all orders between 200 and 400. To see the power of the theorems look for example at the results of Theorem 0.3.