87 
We have the derived groups 
3692581470 cf a dgbehjil It q p n m G 
692581 4703 fadybehc i l kj p n m q 
9258147036 a dgbehcflkji n m q p 
9876543210 abode f g h ijkl m n p q =0 a G 
87654321 09 bcdefghajklinpqm 
7654321098 c d ef g h a b k l i j p q m n 
741 8529630 cfadgbehjilk q p m n =0 3 G. 
4 1 8 5 2 9 6 3 0 7 fadgbehc ilk j pm n q 
1 8 5 2 9 6 3 0 7 4 a d g b e h cf l k j i m n q p 
which form with the group G a group of 160 substitutions. 
We can form 4 2 different 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 
N— * * T*D> 
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 
