Fitnctions given by Groups. 337 



any one value, Fe, of a /^-valued function Y oi n letters, I 

 will so write F^ that, when exponents are all effaced, it 

 shall be exactly a group containing unity, whose derivates 

 under S just effaced shall be the remaining k-\ values 

 of F. 



I am inclined to believe that the only datum really 

 necessary for the finding all such functions F, whatever 

 they may be, is one only written out of the Q equivalent 

 maximum groups, say the cyclical group containing 

 234. ..(;2— \) n 1 \ but, that the method from such datum, 

 if practicable, would be briefer in exposition and easier in 

 practice than that given in the preceding expansion of 

 M.M. pp. 342, 343, requires to be proved. 



