On the Relatively Abelian Corpora. 



25 



We close the present section with tlie following list of the 

 divisors of Jv(.v^. 



§. 8. 



Before proceeding to the discnssion of the division of periods 

 of sn l)y powers of /^, let us insert here a digression on the classes 

 of congruent integers in an algebraic corpus. 



Let p" he a power of a prime ideal in an algebraic corpus. 

 The integers in the corpus can be classified into classes of congru- 

 ent integers w^ith respect to the modulus p\ These classes can be 

 composed with one another by multiplication, They form an 

 Abelian proup of order ^^-'^"-^^ (/>'' — l), wdiere ^ is a natural prime 

 divisible l)y p, and/ the degree of p. 



The problem of determining the rank and the invariants of 

 this group has already been solved to some extent by G. Wolfï'^ 

 and by the present author."' The result obtained by the latter is 

 as follows. 



The Abelian group in question can be decomposed into two 

 component subgroups 31 and 35 of orders ^:)-^("-i) and 75-^—1 respec- 

 tively. 



1) Wolff: Ueber Gruppen der Reste eines beliebigen Moduls im algeraischen Zahl- 

 kürper (Dissertation ; Giesson, 1905). 



2) Takenoiichi: Journal of the College of Science, Tokyo Imperial University, Vol. 

 XXXVI, Art. 1. 



