87 



We have the derived groups 

 3692581470 cfadgh eh jilh qpnm =01 G 

 &^2 o%\ 4:1 OZ fadgh ehc ilkj pnmq 

 9258147036 adghehcflhjinmqp 



9876543210 ahcd efg h ij hi mnpq =9^ G 

 8765432109 bed efg ha jkli np q m 

 7654321098 cd efg hah hi ij p qmn 



7418 5 29630 cfa dgb eh j ilk q p m 7i =QJ3[. 

 4.1 S 5 29 6S0 7 fadg behc ilkj pmnq 

 18 5 2 9 6 3 7 4 adgbehcflkji mnqp 



which form with the group G a group of 160 substitutions. 

 We can form 4] diiferent such groups on this group G, with 

 this root 3. 



I believe that this theor. K is new. 

 (89) Theor. L. 



Let J be any group of Kr substitutions formed with N 

 elements on the partition 



being composed of any a equivalent groups, the same or 

 different, formed each with A elements, of any b equivalent 

 groups formed each with B elements, etc. ; these equivalent 



