Nilpotent Groups and their Automorphisms
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Nilpotent Groups and their Automorphisms

  1. 266 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Nilpotent Groups and their Automorphisms

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Information

Publisher
De Gruyter
Year
2011
ISBN
9783110846218
Edition
1
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Notation
  2. Preface
  3. Part I Linear Methods
  4. Chapter 1. Preliminaries
  5. § 1.1 Groups
  6. § 1.2 Rings and modules
  7. § 1.3 Lie rings
  8. § 1.4 Mappings, homomorphisms, automorphisms
  9. § 1.5 Group actions on a set
  10. § 1.6 Fixed points of automorphisms
  11. § 1.7 The Jordan normal form of a linear transformation of finite order
  12. § 1.8 Varieties and free groups
  13. § 1.9 Groups with operators
  14. § 1.10 Higman’s Lemma
  15. Chapter 2. Nilpotent groups
  16. § 2.1 Commutators and commutator subgroups
  17. § 2.2 Definitions and basic properties of nilpotent groups
  18. § 2.3 Some sufficient conditions for soluble groups to be nilpotent
  19. § 2.4 The Schur-Baer Theorem and its converses
  20. § 2.5 Lower central series. Isolators
  21. § 2.6 Nilpotent groups without torsion
  22. § 2.7 Basic commutators and the collecting process
  23. § 2.8 Finite p-groups
  24. Chapter 3. Associated Lie rings
  25. § 3.1 Results on Lie rings analogous to theorems about groups
  26. § 3.2 Constructing a Lie ring from a group
  27. § 3.3 The Lie ring of a group of prime exponent
  28. § 3.4 The nilpotency of soluble Lie rings satisfying the Engel condition
  29. Part II Automorphisms
  30. Chapter 4. Lie rings admitting automorphisms with few fixed points
  31. § 4.1 Extending the ground ring
  32. § 4.2 Regular automorphisms of soluble Lie rings
  33. § 4.3 Regular automorphisms of Lie rings
  34. § 4.4 Almost regular automorphisms of prime order
  35. § 4.5 Comments
  36. Chapter 5. Nilpotent groups admitting automorphisms of prime order with few fixed points
  37. § 5.1 Regular automorphisms of prime order
  38. § 5.2 Nilpotent p-groups with automorphisms of order p
  39. § 5.3 Nilpotent groups with an almost regular automorphism of prime order
  40. § 5.4 Comments
  41. Chapter 6. Nilpotency in varieties of groups with operators
  42. § 6.1 Preliminary lemmas
  43. § 6.2 A nilpotency theorem
  44. § 6.3 A local nilpotency theorem
  45. § 6.4 Corollaries
  46. § 6.5 Comments
  47. Chapter 7. Splitting automorphisms of prime order and finite p-groups admitting a partition
  48. § 7.1 The connection between splitting automorphisms of prime order and finite p-groups admitting a partition
  49. § 7.2 The Restricted Burnside Problem for groups with a splitting automorphism of prime order
  50. § 7.3 The structure of finite p-groups admitting a partition and a positive solution of the Hughes problem
  51. § 7.4 Bounding the index of the Hughes subgroup
  52. § 7.5 Comments
  53. Chapter 8. Nilpotent p-groups admitting automorphisms of order pk with few fixed points
  54. § 8.1 An application of the Mal’cev correspondence
  55. § 8.2 Powerful p-groups
  56. § 8.3 A weak bound for the derived length
  57. § 8.4 A strong bound for the derived length of a subgroup of bounded index
  58. References
  59. Index of names
  60. Subject Index