I'm not sure I understand what Wikipedia means here. What makes a solvable group of a given order "maximal" ? The fact that it's solvable implies its composition factors are Z/2Z, Z/3Z, Z/7Z. It could be Z/42Z or S_3 x Z/7Z or maybe some other things. And whatever maximal means, does there always exist a unique maximal solvable group of a given order (as "the maximal" below implies for 42) ? --Dan RWG mentioned: << http://en.wikipedia.org/wiki/Septic_equation sez "The Galois group <http://en.wikipedia.org/wiki/Galois_group> of this septic is the maximal solvable group of order 42."
________________________________________________________________________________________ It goes without saying that .