108 



If = 0, then d 



w = 



CHAPTER II. 



1 and the transformed of F by -Ri )TO , y^ 1 gives 



7n 



y- 1 00 



000 - d^ 



r.T 1 ^- 1 



If 0=[=0, the transformed of F by JVi, m> ^ gives a substitution of 

 the form W. Since TF is the product of a substitution on the 

 indices 1? 7^ and a substitution on the indices % mj i] m , it is conjugate 

 with MiM m . 



= (* = 2, 

 = 0, we get 



1 







1). 



02m 



Transforming 1L[ by i 5 m> ff , we obtain a substitution X" which differs 

 from Zj^ only in having the coefficients + 1 replaced by + (1 20a n ). 

 By choice of 6, the latter may be made zero. Hence Z'^ = S^S', 

 where S affects only J t , ^ and is therefore conjugate with M v 

 while 5 ; affects only /, 7^; (* = 2, . : ., m) and is, by assumption, 

 conjugate with Jf 2 -^3 ^m- Hence Z'^ is conjugate with 



MM 2 ... M. 



