91 



123 564 789 



123 564 897 



123 564 978 



123456879 



123 456 987 



123 456 798 

 Let tbis woven group of the order 6' be Jj ; then 

 J^+Qi Ja+QzJa is a grouped woven group of 648th order. 

 (99) Theorem M. 



Let N=A«-i-BHCc+ . , +J;' ; 



A-B B-C C-D 



Let Mb be the number of groups equivalent to a group G , 

 (including G^ in this number) formed with R elements, of S^ 

 substitutions, and such that G.i shall not be equivalent to G^ 

 even though A=r B. 



Let Fr be the entire number of groups, of/,, substitutions, 

 that can be formed (containing unity) with r elements. 



We can construct with N elements, upon the given partition 

 of N, and with given groups G,i G^ * * G/, 



ttN • F„ F, F, ' • F, (yhYiMMMaY' • ' (Ujy 

 Tra' Trb • TTC" ttJ ' (^A)" (B)'^ {"^'^'f ' ' (''"J/ 



woven grouped groups each of 



substitutions. 



For example, on the partition, 



10=::3 • 2 + 2-2=:Aa + BS, 

 where we have 



M3=1 = M2 = F2, 

 we can form 



""' , = 6300 



2 • 2 • 62 • 2- 

 woven grouped groups, each 



32 . 22 . 2 • 2 = 144 substitutions, (8^ = 3), 

 ot of 



g2 . 2^ . 2 • 2 = 576 substitutions, (S^= 6). 



