Hence when we would have exhausted all possible proper decompositions on the group of an equation, we arrive at groups which can be transformed but for whichthe number of permutations will always be the same. If each of these groups has a prime number of permutations then the equation will be solvable by radicals; otherwise, not. The smallest number of permutations that an indecomposable group can have,when this number is not a prime number, is 5・4・3.（＝60のA5(交代群)） (引用終り) 以上
