TABLE OF CONTENTS. IX 



CHAPTER Xm. 



Auxiliary theorems on abstract groups. Abstract forms 

 of various linear groups. 



Section Page 



264 267. Abstract groups isomorphic with the symmetric and alter- 

 nating groups 287 290 



268 269. Quaternary linear group modulo 2 isomorphic with the 



alternating group on 8 letters 290 292 



270 274. Abstract form of quinary orthogonal group modulo 3 . . 292 298 



275 276. Its isomorphism with a hyperabelian group 298 299 



278282. Abstract group isomorphic with LF(Z,pn} 300303 



CHAPTER XIV. 



Group of the equation for the 27 straight lines on a general 

 surface of the third order. 



283. Notation for the configuration of the 27 lines 303 305 



284 285. Group of the equation. Isomorphism with linear groups . 305 306 



286. Subgroups of indices 27, 36, 40, 45 306307 



CHAPTER XV. 

 Summary of the known systems of simple groups. 



287. The ten known infinite systems . . 307 



288. Isomorphisms between certain groups of the systems . . 308 



289. Two triply infinite systems of non- isomorphic simple groups 



of equal order 309 



290. Table of simple groups of orders less than a million . . 309 310 



INDEX OF SUBJECTS . 311-312 



