M.-p.— Vol. I.] DICKSON— THE ORTHOGONAL GROUP. 



49 



2 

 -I 



-r 



-i 

 i 



2 



-T 



2 

 I 



= R ] Ci Co /?. 



The variations from the proof of the theorem of § 4 of my 

 paper, necessary for the case fi n = 5, are the following. 

 Instead of applying the lemma in § 6 (which becomes trivial 

 for^ 11 = 5), we note that the transformed of C\ C- 2 by R is 

 not a product of the C\ (as shown by the above formula). 

 We may omit §11. For p. 36 we note that the value p 2 = 1 

 may be chosen, the right member of the equation of condi- 

 tion being then zero. At the end of § 14, when x./3 = o, I 

 contains C x C 2 and thus, by the above formula, also the 

 substitution 



R Z12 7^3 = 



if we take a x = cr 2 = °"3 



211 

 112 

 121 



Sn- 71 



23 



2, so that 



= 2 



O"; cr. = I 



5. We pass next to the case p u = 3. 



For m = 3, the group H is the composite group 



Gu = { 1, C, ^ (three), T 4 T ik (two), T x] T ik C t C, (six) } . 



For w>3, the total group (? may be generated b}^ the 

 C\ C; and T„ C v together with the substitution* of deter- 

 minant -\-i : 



w 



2 

 I 



2 



I 



W* = W -x = Cl WCx 



The C-, Cj generate a group of order 



,m— 1 



m (m — 1) m (m — 1) (m — 2) (m — 3) 



1.2 I.2.3.4 



* In the theoram given on p. 30 of my earlier paper, p n ^ 5 should read 

 p n >$. The case p n = 3 was not observed to be special until it was noticed 

 that in Jordan, $211, case 2" is proved only when — 1 is a not-square. The 

 case 3' 1 , n > 1, can be readily disposed of. 



