PrefaceConventions and Notation1 Preliminaries1.1 Group actions1.2 Normal subgroups, automorphisms, characteristic subgroups, simple groups1.3 Filtrations and Jordan-H？lder theorem1.4 Subgroups of products: Goursats lemma and Ribets lemma1.5 Exercises2 Sylow theorems2.1 Definitions2.2 Existence of p-Sylow subgroups2.3 Properties of the p-Sylow subgroups2.4 Fusion in the normalizer of a p-Sylow subgroup2.5 Local conjugation and Alperins theorem2.6 Other Sylow-like theories2.7 Exercises3 Solvable groups and nilpotent groups3.1 Commutators and abelianization3.2 Solvable groups3.3 Descending central series and nilpotent groups3.4 Nilpotent groups and Lie algebras3.5 Kolchins theorem3.6 Finite nilpotent groups3.7 Applications of 2-groups to field theory3.8 Abelian groups3.9 The Frattini subgroup3.10 Characterizations using subgroups generated by two elements3.11 Exercises4 Group extensions4.1 Cohomology groups4.2 A vanishing criterion for the cohomology of finite groups4.3 Extensions, sections and semidirect products4.4 Extensions with abelian kernel4.5 Extensions with arbitrary kernel4.6 Extensions of groups of relatively prime orders4.7 Liftings of homomorphisms4.8 Application to p-adic liftings4.9 Exercises5 Hall subgroups5.1 -subgroups5.2 Preliminaries: permutable subgroups5.3 Permutable families of Sylow subgroups5.4 Proof of theorem 5.15.5 Sylow-like properties of the -subgroups5.6...... 全部内容请购买实物书籍
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