as depending on the Symbolic Equation d" = l. 



45 



while if we represent the second of these two forms, viz. the 



group 



1, «, a^ 7, a7, «^7, {a?=\, ^'^-\, ^a. = a"^), 



by the same general symbols 



1, «; A 7^ ^> ^} 

 we have the table 



1 « /3 7 S 6 



or, what is the same thing, the system of equations 

 l=y3« = «/3 = 72 =82 = e2 

 a = /8'^ =87 =e8 =7e 

 /3 = «2 =67 =78 =Se 

 7=8« =e/3 =/3S = ci6 

 8 = e« =y/8 = ay = ^e 

 e = ya=8/3=/3y = a8. 

 An mstance of a group of this kind is given by the pcrmuta- 



