90 
Neither the group of 18 nor that of 38 can be presented as 
a grouped group of K/ substitutions of theorem H, like 
the following of K l 
123 456 789 
231 564 897 
312 6 45 978 
456 789 123 
564 897 231 
645 978 312 
= 8*3 substitutions. 
789 123 456 
897 231 564 
978 312 646 
123 789 456 
231 897 564 
312 978 645 
789 456 123 
897 564 231 
978 312 645 
456 123 789 
564 231 897 
645 312 978 
Woven Groups. 
(95) “ Let N = A + B. 
Let G be any group of L substitutions, formed with A 
elements, and G 1 , be any group of L 1 substitutions formed with 
B elements following the A in unity. We can always form 
a woven group of LL 1 substitutions. There is nothing to 
prevent G and G 1 being themselves woven groups. 
e. g. the two woven groups : — 
1 2 3 4 5 and 6 7 8 9 
23145 7689 
31245 6798 
12354 7698 
2 3 15 4 
3 12 5 4 
will form a woven group of 24 substitutions.” 
Woven Grouped Groups. 
(96) The grouped group J-fQi J+Q 2 J of (89) of3 , 2 , 3= 
krl substitutions can become a woven grouped group of 
6 3, 3=648 substitutions. For 
of G 3 , thus : 
123 456 789 
123 456 897 
123 456 978 
123 456 879 
123 456 987 
123 456 798 
can be woven into a group 
123 546 789 
123 546 897 
123 546 978 
123 546 879 
123 546 987 
123 546 798 &c. 
