25 Finite Polycyclic Groups

Ag groups (see Words in Finite Polycyclic Groups) are a subcategory of finitely generated groups (see Groups).

The following sections describe how subgroups of ag groups are represented (see More about Ag Groups), additional operators and record Ag Group Functions and Subgroups and Properties of Ag Groups). Some additional information about generating systems of subgroups and factor groups are Factor Groups of Ag Groups.

One Cohomology Group describes how to compute the groups of one coboundaries and one cocycles for given ag groups. Complements gives informations how to obtain complements and conjugacy classes of complements for given ag groups.

Subsections

  1. More about Ag Groups
  2. Construction of Ag Groups
  3. Ag Group Operations
  4. Ag Group Records
  5. Set Functions for Ag Groups
  6. Elements for Ag Groups
  7. Intersection for Ag Groups
  8. Size for Ag Groups
  9. Group Functions for Ag Groups
  10. AsGroup for Ag Groups
  11. Group for Ag Groups
  12. CommutatorSubgroup for Ag Groups
  13. Normalizer for Ag Groups
  14. IsCyclic for Ag Groups
  15. IsNormal for Ag Groups
  16. IsSubgroup for Ag Groups
  17. Stabilizer for Ag Groups
  18. CyclicGroup for Ag Groups
  19. ElementaryAbelianGroup for Ag Groups
  20. DirectProduct for Ag Groups
  21. WreathProduct for Ag Groups
  22. RightCoset for Ag Groups
  23. FpGroup for Ag Groups
  24. Ag Group Functions
  25. AgGroup
  26. IsAgGroup
  27. AgGroupFpGroup
  28. IsConsistent
  29. IsElementaryAbelianAgSeries
  30. MatGroupAgGroup
  31. PermGroupAgGroup
  32. RefinedAgSeries
  33. ChangeCollector
  34. The Prime Quotient Algorithm
  35. PQuotient
  36. Save
  37. PQp
  38. InitPQp
  39. FirstClassPQp
  40. NextClassPQp
  41. Weight
  42. Factorization for PQp
  43. The Solvable Quotient Algorithm
  44. SolvableQuotient
  45. InitSQ
  46. ModulesSQ
  47. NextModuleSQ
  48. Generating Systems of Ag Groups
  49. AgSubgroup
  50. Cgs
  51. Igs
  52. IsNormalized
  53. Normalize
  54. Normalized
  55. MergedCgs
  56. MergedIgs
  57. Factor Groups of Ag Groups
  58. FactorGroup for AgGroups
  59. CollectorlessFactorGroup
  60. FactorArg
  61. Subgroups and Properties of Ag Groups
  62. CompositionSubgroup
  63. HallSubgroup
  64. PRump
  65. RefinedSubnormalSeries
  66. SylowComplements
  67. SylowSystem
  68. SystemNormalizer
  69. MinimalGeneratingSet
  70. IsElementAgSeries
  71. IsPNilpotent
  72. NumberConjugacyClasses
  73. Exponents
  74. FactorsAgGroup
  75. MaximalElement
  76. Orbitalgorithms of Ag Groups
  77. AffineOperation
  78. AgOrbitStabilizer
  79. LinearOperation
  80. Intersections of Ag Groups
  81. ExtendedIntersectionSumAgGroup
  82. IntersectionSumAgGroup
  83. SumAgGroup
  84. SumFactorizationFunctionAgGroup
  85. One Cohomology Group
  86. OneCoboundaries
  87. OneCocycles
  88. Complements
  89. Complement
  90. Complementclasses
  91. CoprimeComplement
  92. ComplementConjugatingAgWord
  93. HallConjugatingWordAgGroup
  94. Example, normal closure
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GAP 3.4.4
April 1997