Theory and applications of finite groups, by G.A. Miller, H. F. Blichfeldt [and] L. E. Dickson.

xiv

TABLE OF CONTENTS

SECTION PAGE
65. Groups of isomorphisms of the alternating and the symmetric groups.... 166
E xercises....................................................... 168
66. Several useful theorems relating to groups of isomorphisms............. 168
67. Group of isomorphisms of a transitive substitution group.............. 172
Exercises......................................... 173
CHAPTER VIII
SOLVABLE GROUPS
68. Introduction..................................................... 174
E xercises........................................................ 177
69. Series of composition.......................................... 177
70. Groups involving no more than one non-cyclic Sylow subgroup......... 181
71. Groups whose nth group of inner isomorphisms is the identity.......... 183
Exercises........................................................ 184
72. Arbitrary choice of factors of composition........................... 184
'73. Groups of order paq3, p and q being prime numbers.................. 185
74. Insolvable groups of low composite orders........................... 186
Exercises...................................................... 192
PART II
FINITE GROUPS OF LINEAR HOMOGENEOUS TRANSFORMATIONS
CHAPTER IX
PRELIMINARY THEOREMS
75-82. Linear transformations; product of linear transformations........ 193
83-7. Groups of linear transformations................................. 197
88. Change of variables............................................ 203
89. Characteristic equation......................................... 205
90. Transitive and intransitive groups................................ 206
91-3. Hermitian invariant; conjugate-imaginary groups; unitary form..... 207
94. Reducible and irreducible groups.................................. 210
95-6. Canonical form of a linear transformation and of abelian groups.... 212
CHAPTER X
THE LINEAR GROUPS IN TWO VARIABLES
97-100. Introduction; geometrical analysis............................. 215
101-3. The groups of the regular polyhedra............................. 220.04-5. Invariants of the linear groups in two variables.,..,....;... 224