Theory of Groups

Cover
S Title
THE THEORY OF GROUPS
Copyright
     © 1971 by Addison-Wesley Publishing Company
Dedication
PREFACE
CONTENTS
1  BASIC CONCEPTS AND NOTATION
2  PRODUCTS; DIRECT PRODUCTS; DIRECT PRODUCT WITH AMALGAMATED SUBGROUP; AND SUBDIRECT PRODUCTS
     2.1 PRODUCTS AND DIRECT PRODUCTS
          EXERCISES 2.1
     2.2 DIRECT PRODUCT WITH AMALGAMATED SUBGROUP
          EXERCISES 2.2
     2.3 SUBDIRECT PRODUCTS
          Exercises 2.3
3  SPLITTING EXTENSIONS; SEMIDIRECT AND WREATH PRODUCTS
     3.1 PRODUCTS OF SUBGROUPS
          EXERCISES 3.1
     3.2 EXTENSIONS
          EXERCISES 3.2
     3.3 SPLITTING EXTENSIONS
          EXERCISES 3.3
     3.4 WREATH PRODUCTS
          EXERCISES 3.4
4  THEOREMS ON SPLITTING; HALL SUBGROUPS
     4.1 ON A THEOREM OF DIXON
          EXERCISES 4.1
     4.2 SPLITTING THEOREMS OF GASCHUTZ
          EXERCISES 4.2
     4.3 ON HALL n-SUBGROUPS
          EXERCISES 4.3
     4.4 ADDITIONAL COMMENTS
          EXERCISES 4.4
5  NILPOTENT GROUPS; THE FRATTINI SUBGROUP
     5.1 NILPOTENT GROUPS
          EXERCISES 5.1
     5.2 THE SYLOW STRUCTURE OF A NILPOTENT GROUP
          EXERCISES 5.2
     5.3 THE FRATTINI SUBGROUP
          EXERCISES 5.3
     5.4 ADDITIONAL REMARKS ON THE FRATTINI SUBGROUP
          EXERCISES 5.4
6  THE FITTING SUBGROUP; SUPERSOLV ABLE GROUPS
     6.1 THE FITTING SUBGROUP
          EXERCISES 6.1
     6.2 SUPERSOLVABLE GROUPS
          EXERCISES 6.2
7  GENERAL EXTENSION THEORY
     7.1 EXTENSIONS AND FACTOR SETS
          EXERCISES 7.1
     7.2 EQUIVALENT EXTENSIONS
          EXERCISES 7.2
     7.3 EXTENSIONS OF ABELIAN GROUPS
          EXERCISES 7.3
     7.4 CYCLIC EXTENSIONS
          EXERCISES 7.4
     7.5 FINITE EXTENSIONS OVER A CYCLIC MAXIMAL SUBGROUP OF PRIME POWER ORDER
          EXERCISES 7.5
8  THE THEORY OF THE TRANSFER
     8.1 THE TRANSFER
          EXERCISES 8.1
     8.2 BURNSIDE'S THEOREM
          EXERCISES 8.2
     8.3 THE THEOREMS OF GRUN
          EXERCISES 8.3
     8.4 SOME APPLICATIONS OF THE THEOREMS OF GRUN
          EXERCISES 8.4
9  FREE GROUPS AND COPRODUCTS
     9.1 FREE GROUPS
          EXERCISES 9.1
     9.2 FREE PRODUCTS AND COPRODUCTS IN Grp
          EXERCISES 9.2
     9.3 COPRODUCTS IN Ab
          EXERCISES 9.3
APPENDIX  SOME ELEMENTS OF CATEGORY THEORY
     A.l   CATEGORIES AND FUNCTORS
          EXERCISES A.1
     A.2  PRODUCTS AND COPRODUCTS
          EXERCISES A.2
BIBLIOGRAPHY AND INDEX OF SPECIAL SYMBOLS
     BIBLIOGRAPHY
     INDEX OF SPECIAL SYMBOLS
INDEX
     INDEX