154 UNIVERSITY OF COLORADO STUDIES 



The type groups are 



A x k = poc=pa = p/3 = p,the Abelian group of type (m — 2, 1, 1) 



A 2 , k=i oc = p a = p y8 = p 



A 4 , k = p oc =p a = i /8 = p 



B x , k = p oc = p a = p f3 = 1 



B a , k = 1 oc = p a = p (3=i 



B 4 . k = p oc = p a = 1 /? = 1 



Page 2 g6: In A, , A a , B, , B a : 



VI. a' x = o (mod p) 

 Leave out 



Elimination between V and VI gives 



oc ' —a' (3' = (mod p) 

 Page 2Q? : Leave out Case B 3 and insert A 4 and B 4 . 



A 4 



I. a (y z — y' z) = k' x (mod p) 



III. /?' z' = o (mod p) 



IV. y8'y' = o (mod p) 



V. a(yz"— y"z) = oc ' x (mod p) 



VI. a(y'z"— y"z') = a' x (mod p) 



B 4 



z (z — 1^ 



I. a (3 x 1- a (y z' — y ' z) = k' x (mod p) 



II. j8xz'Eo (mod p) 



III. /3' z' = o (mod p) 



IV. /3'y' = /?+z" (modp) 



V. affx 2 (Z ~ *) + a (yz' , -y ,, z) = oc'x + /3'x' 



+ a (3' y' z (mod p) 



VI. a (y' z"— y" z') = a' x mod p) 



