NORMAL FORMS. 197 
$6. Normal Forms of Groups of Type I. 
We shall now return to the theory of the groups of type I 
and continue by the use of the normal form of T the discus- 
sion of those groups begun in $4 by means of the homogen- 
eous form of 7. We shall express the relations R,, R,, R,., 
etc., in the normal form of T and deduce therefrom many im- 
portant results, the chief of which are what we shall call the 
k-relations. 
The normal form of 7 will be taken with the proportionality 
factor p equal to unity, thus: 
LAU 2 0 | 
pede 
All BY CRA" | 
Care must be taken as before to exclude from the discussion 
the form T, viz.: 
eyE ee 0 
ANB RG iA 
A’ BY Ct kay |» CLC. 
A” BY CU WAY 
i 
230. Normal Form of R,. Using the normal form of the 
collineation T, page 104,, the linear relations FR, defining the 
group G,(A) become: 
Bc A PMO AGRE ACA a eet 
YB ov wan) lan on war) "an ge war] |AlB O ar |=! 
; i 7 : Al’ BY Cl RIAU 
he GC) 2B ANC (iB Ay BRB ie a 2] 
180 te mia C48 tua ate 88 Sk mm 
: ; ‘ A!’ Bt (Ou k/B" 
(41) 
5 KGa MG} lg (A EI AgEB™ aC i eh ea 
L}B Cc’ kC’|—m| A’ Coke 4+ n/a BY ke =| 4, Gy Gy | =. 
| Br Cc! kc” A” Cl’ kc" All BY kG” | | 
All Bil (Oi k’cv | 
