Sylow theory, formations and fitting classes in locally finite groups

✍ Scribed by Martyn R. Dixon

• Publisher: World Scientific
• Year: 1994
• Tongue: English
• Leaves: 317
• Series: Series in Algebra, Vol. 2
• Category: Library

✦ Table of Contents

Front Matter......Page 1
Series in Algebra......Page 2
COVER......Page 3
Preface......Page 5
1.1. Group Theoretical Classes and Closure Operations......Page 14
1.2. Series of Subgroups......Page 19
1.3. Radicals and Residuals......Page 26
1.4. Local Systems......Page 31
1.5. The Minimum Condition and Černikov Groups......Page 40
1.6. Generalizations of the Minimum Condition......Page 48
1.7. Some Miscellaneous Results......Page 59
2.1. Introduction......Page 66
2.2. Elementary Results and Examples......Page 67
2.3. Conjugacy and the Size of |Syl_π G|......Page 78
2.4. The Asar-Hartley Theorem for a General Set of Primes......Page 89
2.5. Groups with min-p......Page 95
2.6 Good Sylow Subgroups......Page 106
3.1. Sylow Theory in Groups with min-p for all Primes p......Page 112
3.2. Locally Soluble Groups of Finite Rank......Page 117
3.3. Some Properties of PSL(2, F)......Page 123
3.4, The 2-radicable Part of a Group with min-p for all p......Page 127
3.5. The Structure of Groups with min-p for all Primes p......Page 138
4.1. Upper π-separable Groups......Page 154
4.2. Groups with the Minimum Condition on Centralizers......Page 157
4.3. The Structure of Sylow p-integrated Groups......Page 171
4.4. Completely Sylow Integrated Groups......Page 173
4.5. Metabelian Groups with min-n......Page 178
5.1. General Properties of Sylow Bases......Page 182
5.2. Sylow Bases in U-groups......Page 188
5.3. Sylow Bases in Groups with min-p for all p......Page 194
5.4. Further Results on Groups with min-p for all p......Page 201
5.5. Co-Hopfian Groups......Page 209
6.1. A Brief Historical Account......Page 218
6.2. Locally Defined Formations......Page 220
6.3. The F-normalizers of Locally Finite Groups......Page 229
6.4. F-projectors in Locally Finite Groups......Page 243
6.5 Concluding Remarks Concerning Formation Theory......Page 258
7.1. A Brief Historical Account......Page 264
7.2. Elementary Properties of Fitting Classes......Page 265
7.3. Injectors in Locally Finite Groups......Page 270
7.4. Injectors in Groups with min-p for all Primes p......Page 278
7.5. Conjugacy Conditions for Injectors in L-groups......Page 285
7.6. Closing Remarks......Page 293
Bibliography......Page 296
Index......Page 312