182 



CHAPTER VII. 



y v 



-M4 J -23 



24 



/3 2 up aft -a 2 

 _ a/3 _02 _ K 2 _ a/3 



a/3 -a 2 -/3 2 a/3 

 -a 2 -a/3 a/3 /3 2 



and is the second compound of the special Abelian substitution 



P a ( 



a -/3 



/3 -a 



-a -/3j 



Hence $1 contains OajJOils. We next show that (^ contains the 

 linear substitution (i 2 i 4 | 8 ), so that with (ii^is) 61 w ^ contain all 

 even substitutions on | 1? . . ., J 5 . Expressing (Ig^ls) i n the indices Y/y, 

 we get 



3, 



requires an additional generator W 1234 . For 



a = /3 == 1, the following substitution 



