TABLE OF CONTENTS. VH 



CHAPTER III. 

 A generalization of the Abelian linear group. 



Section Page 



124 125. Definition of the substitutions; their inverse 110 111 



126128. Structure of the group 111114 



CHAPTER IY. 

 The Tiyperdbelian group. 



129 130. Conditions on its substitutions; their inverse 115 116 



131. Largest subgroup containing the Abelian group self- 



conjugately 117120 



132 133. Corresponding theorems for their quotient -groups . . . 120 121 

 134 136. Binary linear homogeneous subgroups of the quaternary 



hyperabelian group. Application to their quotient -groups 122 125 



137. Identity of binary hyperabelian and binary linear group . 125 



CHAPTER V. 

 The hyperorthogonal and related linear groups. 



139 142. Definition. Structure in the general case 126 131 



143 151. Order, generators and structure in the hyperorthogonal case 131 144 



CHAPTER VI. 

 The compounds of a linear homogeneous group. 



153. Isomorphism of linear group with its compounds . ... 145 146 



154. Multiplicity of isomorphism for general linear group . . 146 147 

 156. Pfaffian invariant of the second compound 147 148 



157 158. Group induced upon certain Pfaffians by the second compound 148 150 

 159 162. The second compound of the general and special Abelian 



groups , 151 153 



163 165. The second compound of the quaternary linear group , . 153 155 



CHAPTER VE. 



Linear homogeneous group in the GF[p], p > 2, 

 defined ~by a quadratic invariant. 



166 169. Canonical forms of the quadratic invariant 156 158 



170171. Orthogonal substitutions; the first and second orthogonal 



groups 159 



172 180. Order and generators of the orthogonal groups .... 160 169 

 178. The ternary first orthogonal group and the linear fractional 



group 164 



181198. The structure of the orthogonal groups 169197 



186 188. Senary orthogonal groups isomorphic with quaternary 



linear groups 172 179 



189. Quinary orthogonal group isomorphic with quaternary 

 Abelian group 179182 



190. Senary orthogonal groups isomorphic with hyperabelian 



groups 183186 



195 198. Quaternary orthogonal and linear fractional groups . . . 191 196 



