GAP Manual: 51. Maps and Parametrized Maps

In this chapter, first the data structure of (parametrized) maps is introduced (see More about Maps and Parametrized Maps). Then a description of several functions which mainly deal with parametrized maps follows; these are

basic operations with paramaps (see CompositionMaps, InverseMap, Indirected, ProjectionMap, Parametrized, ContainedMaps, UpdateMap, CommutativeDiagram, TransferDiagram),

functions which inform about ambiguity with respect to a paramap (see Indeterminateness, PrintAmbiguity),

functions used for the construction of powermaps and subgroup fusions (see Powermap, SubgroupFusions and their subroutines InitPowermap, Congruences, ConsiderKernels, ConsiderSmallerPowermaps, PowermapsAllowedBySymmetrisations, InitFusion, CheckPermChar, CheckFixedPoints, TestConsistencyMaps, ConsiderTableAutomorphisms, FusionsAllowedByRestrictions, OrbitPowermaps, OrbitFusions, RepresentativesPowermaps, RepresentativesFusions, Powmap) and

the function ElementOrdersPowermap.

This chapter contains the following sections:

• 51.1. More about Maps and Parametrized Maps
• 51.2. CompositionMaps
• 51.3. InverseMap
• 51.4. ProjectionMap
• 51.5. Parametrized
• 51.6. ContainedMaps
• 51.7. UpdateMap
• 51.8. CommutativeDiagram
• 51.9. TransferDiagram
• 51.10. Indeterminateness
• 51.11. PrintAmbiguity
• 51.12. Powermap
• 51.13. SubgroupFusions
• 51.14. InitPowermap
• 51.15. Congruences
• 51.16. ConsiderKernels
• 51.17. ConsiderSmallerPowermaps
• 51.18. InitFusion
• 51.19. CheckPermChar
• 51.20. CheckFixedPoints
• 51.21. TestConsistencyMaps
• 51.22. ConsiderTableAutomorphisms
• 51.23. PowermapsAllowedBySymmetrisations
• 51.24. FusionsAllowedByRestrictions
• 51.25. OrbitFusions
• 51.26. OrbitPowermaps
• 51.27. RepresentativesFusions
• 51.28. RepresentativesPowermaps
• 51.29. Indirected
• 51.30. Powmap
• 51.31. ElementOrdersPowermap