VIU TABLE OF CONTENTS. 



CHAPTER 



Linear homogeneous group in the GF[2 n \ defined 



by a quadratic invariant. 

 Section . Page 



199. Canonical forms of the quadratic invariant ...... 197 199 



200. Structure of group on an odd number of indices .... 199200 

 201204. Definition, order and generators of the hypoabelian 



groups ................... 200206 



205. Invariant defining the subgroup JA ......... 206 208 



206208. Isomorphism of senary group Ji with certain quaternary 



groups ................... 208211 



209. Simplicity of Ji on more than six indices ...... 212216 



210. Miscellaneous exercises on chapters I VIII ...... 216 218 



CHAPTER IX. 



Linear groups with certain invariants of degree q > 2 . 



211213. Definition, generators and structure of group ..... 218221 



CHAPTER X. 

 Canonical form and classification of linear substitutions. 



214 216. Canonical form of linear homogeneous substitutions . . . 221 229 



217 220. Substitutions commutative with a given linear substitution 229 236 

 221 223. Distribution of the substitutions of the general ternary and 



quaternary linear groups into sets of conjugate substitutions 236241 



CHAPTER XL 



Operators and cyclic subgroups of the simple group 



LF(3,pn). 



224 225. Notations. The seven distinct canonical forms .... 242 244 



226 237. Conjugate operators and cyclic groups of each type . . . 245 259 



238. LF(3, 2 2 ) not isomorphic with the alternating group on 



8 letters, each group being simple and of equal order . . 259260 



CHAPTER XH. 

 Subgroups of the linear fractional group LF(2,pn). 



239. Doubly transitive substitution group on^-f 1 letters . . 260 261 

 240 244. Commutative subgroups of order pn- cyclic subgroups . . 261 265 



245. Concerning dihedron groups and their subgroups .... 265 266 



246 248. Subgroups of dihedron and four- group types ..... 267 268 



249 255. Subgroups containing operators of period p ...... 268280 



256. Subgroups containing no operators of period p . . . . 280 282 



257 259. Subgroups of tetrahedral, octahedral and icosahedral 



types .................... 282285 



260 261. Summary of subgroups. Simplicity theorem ..... 285 286 



262. Galois' theorem on the minimum index of a subgroup . . 286 



263. Lowest degree of isomorphic substitution group .... 287 



