292 UNIVERSITY OF COLORADO STUDIES 



+ -A__aayzp-^ (11) 



Placing z=l y=8=p 



[R P"]" = Rp P^P = P '^+" " 



Tf X be 80 chosen that 



x+l = (mod p"-^) 



RP* is an operator of order p which may be used in place of R. 

 G is generated by P, Q and R 



^m— 2 



PP =1 Qp=l RPz^l 



with relations (1), (7) and (8). 



As a direct consequence of the above these groups correspond 

 to the partition (m — 2, 1, 1). 



When the parameters in (1), (7) and (8) take all possible 

 values consistent with our fundamental assumptions, cases of simple 

 isomorphism between the resulting groups will arise. 



The simply isomorphic groups are reduced to type forms by a 

 transformation. 



Chose a second set of generators P'. Q', and R', then by a 

 repetition of the foregoing argument 



P'P""'=:1 Q'P = 1 R'P=1 



Q'-T'Q'=P'1 + ^'P"~' (12) 



R'-T'R' ^Q'/^'p'l+^'p"'-' (13) 



R'-^Q'R'=Q'P'^'P'""'. (14) 



A consideration of (11) shows that 



P' = R'Q^P^ X not = O(mod p) 



