117 



If we take all ^/ = 0, there belongs to an arbili'ary n-groiip the 

 ??,-gT0iip {I\, . . . , r„); if, however, a point P,- coincides with Ci, 

 the associated point P'i, becomes indefinite, so that to an ?i-group of 

 which the ^ points P,^, Pi^^, . . . , P;^ coincide resp. with Ci^, 6',\,, . . ., C/^. 



there are associated oo^ groups that have the n — k points Pif^,^, ••• , ^«^^ 



in common. 



Let US now consider a system Sk of oo^ ?i-group8 with the ( J 

 characteristic numbers u{^ ,• . . . ,• , indicating how many groups of 

 the system there are for which the points jP,^, P{^, ... , Pi^ are de- 

 fined. Through our representation Sk is traiisfornied into a system *S''/fc 



consisting of ( ) separate systems of oo^* groups. Such a system is 



formed e.g. by the «-groups that have their points Pij^,^, • ■ • > ^j„ 

 resp. in /] , . . . , r, and of which the remaining points P are 

 indefinite. Each group of this system is associated to the «,-^ ,\^ ■ • ■ 'k 

 groups ot Sk that have their points P/^, . . . , Pj^^in Q^ , . . . , C,v, and 

 is therefore an «,• , . . . /,-fold group of S'k- If we take another 

 system S„—k of oo"— ^" groups, with the characteristic numbers 

 i^i i . . . i _,, we find from the number of common groups of 



S'k and Sn-k' 



A system Sk {(^1. • ■ • ij of cc^ n-groups of points has loith a system 



Sn-^k {^i^ ■ ■ ■ .„_ f) of Gc"-^ n-groups ^«/^ . . . /^ ^?/^_j_^ . . . ,;^ groups in 



common. 



Finally we remark that the expounded method may also be 

 applied to curves, surfaces etc. 



8* 



