Fundamentals of the theory of groups
Fundamentals of the theory of groups
复制标题
DOI：
10.2307/3617953
复制
发表时间：
1979
期刊：
影响因子：
--
通讯作者：
Colin R. Fletcher;M. I. Kargapolov;Ju. I. Merzljakov;Robert G. Burns
中科院分区：
文献类型：
--
作者：
Colin R. Fletcher;M. I. Kargapolov;Ju. I. Merzljakov;Robert G. Burns
1 Definition and Most Important Subsets of a Group.- 1. Definition of a Group.- 1.1. Axioms. Isomorphism.- 1.2. Examples.- 2. Subgroups. Normal Subgroups.- 2.1. Subgroups.- 2.2. Generating Sets.- 2.3. Cyclic Subgroups.- 2.4. Cosets.- 2.5. Classes of Conjugate Elements.- 3. The Center. The Commutator Subgroup.- 3.1. The Center.- 3.2. The Commutator Subgroup.- 2 Homorphisms.- 4. Homomorphisms and Factors.- 4.1. Definitions.- 4.2. Homomorphism Theorems.- 4.3. Subcartesian Products.- 4.4. Subnormal Series.- 5. Endomorphisms. Automorphisms.- 5.1. Definitions.- 5.2. Invariant Subgroups.- 5.3. Complete Groups.- 6. Extensions by Means of Automorphisms.- 6.1. The Holomorph.- 6.2. Wreath Products.- 3 Abelian Groups.- 7. Free Abelian Groups. Rank.- 7.1. Free Abelian Groups.- 7.2. Rank of an Abelian Group.- 8. Finitely Generated Abelian Groups.- 9. Divisible Abelian Groups.- 10. Periodic Abelian Groups.- 4 Finite Groups.- 11. Sylow p-Subgroups.- 11.1. Sylow's Theorem.- 11.2. An Application to Groups of Order pq.- 11.3. Examples of Sylow p-Subgroups.- 12. Finite Simple Groups.- 12.1. The Alternating Groups.- 12.2. The Projective Special Linear Groups.- 13. Permutation Groups.- 13.1. The Regular Representation.- 13.2. Representations by Permutations of Cosets.- 13.3. Transitivity. Primitivity.- 5 Free Groups and Varieties.- 14. Free Groups.- 14.1. Definition.- 14.2. A Matrix Representation.- 14.3. Subgroups.- 14.4. The Lower Central Series and the Derived Series.- 15. Varieties.- 15.1. Laws and Varieties.- 15.2. An Alternative Approach to Varieties.- 6 Nilpotent Groups.- 16. General Properties and Examples.- 16.1. Definition.- 16.2. General Properties.- 16.3. Nilpotent Groups of Automorphisms.- 17. The Most Important Subclasses.- 17.1. Finite Nilpotent Groups.- 17.2. Finitely Generated Nilpotent Groups.- 17.3. Torsion-Free Nilpotent Groups.- 18. Generalizations of Nilpotency.- 18.1. Local Nilpotence.- 18.2. The Normalizer Condition.- 18.3. The Engel Condition.- 7 Soluble Groups.- 19. General Properties and Examples.- 19.1. Definitions.- 19.2. Soluble Groups Satisfying the Maximal Condition.- 19.3. Soluble Groups Satisfying the Minimal Condition.- 20. Finite Soluble Groups.- 20.1. Hall and Carter Subgroups.- 20.2. On the Complete Reducibility of Representations.- 20.3. A Criterion for Supersolubility.- 21. Soluble Matrix Groups.- 21.1. Almost-Triangularizability.- 21.2. The Polycyclicity of the Soluble Subgroups of GLn(Z).- 21.3. The Embeddability in GLn(Z) of the Holomorph of a Polycyclic Group.- 22. Generalizations of Solubility.- 22.1. Kuros-?ernikov Classes.- 22.2. Examples.- 22.3. The Local Theorem.- Append.- Auxiliary Results from Algebra, Logic and Number Theory.- 23. On Nilpotent Algebras.- 23.1. Nilpotence of Associative and Lie Algebras.- 23.2. Non-Nilpotent Nilalgebras.- 24. Local Theorems of Logic.- 24.1. Algebraic Systems.- 24.2. The Language of the Predicate Calculus.- 24.3. The Local Theorems.- 25. On Algebraic Integers.- Index of Notations for Classical Objects.
