56 Art. 5. —T. Takenouclii : 



simplicity, we shall hereafter characterise the group Ä, to which 

 the class-corpus K{z{iif) corresponds, by the congruence 



« = 1 (mod. ij). 



It is also known^', tliat the relative degree of the class-corpus 

 corresponding to the group G is not lower than 



~ {EG, G) ' 



where is the group of all the numbers in Jc{p) (of course, taking 

 the excludent into consideration), and (O, G) and {EG, G) denote 

 the indices of G with respect to and EG respectively. If we put 

 G:=A, then 



supposing that A« is associated neither with 2 nor with l+2/>. This 

 value of d coincides with the degree of the equation for ~{nf. 

 Therefore the relative degree of K(j{iif) must l^e exactly equal to 



^(fi'j). AVhen y- is associated with 2 or 1-1- 2/^, the relative degree 



reduces itself to unitv- 



Not only /v(~(»)0' ^^^^ '^^^^ other division-corpora, e.g. K{^{ii)), 

 K(finu), etc., can be looked upon as class-corpora corresj^onding to 

 some groups of numbers. But, as it is not at all necessary for our 

 subsequent investigations, and moreover, as it will occupy too 

 much space, we shall not here enter into a detailed discussion of 

 them. However, it will not be out of place to give here the results 

 I liave arrived at. 



1) Weber : Algebra III, §. 167. 



