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.

Subsections

1. More about Maps and Parametrized Maps
2. CompositionMaps
3. InverseMap
4. ProjectionMap
5. Parametrized
6. ContainedMaps
7. UpdateMap
8. CommutativeDiagram
9. TransferDiagram
10. Indeterminateness
11. PrintAmbiguity
12. Powermap
13. SubgroupFusions
14. InitPowermap
15. Congruences
16. ConsiderKernels
17. ConsiderSmallerPowermaps
18. InitFusion
19. CheckPermChar
20. CheckFixedPoints
21. TestConsistencyMaps
22. ConsiderTableAutomorphisms
23. PowermapsAllowedBySymmetrisations
24. FusionsAllowedByRestrictions
25. OrbitFusions
26. OrbitPowermaps
27. RepresentativesFusions
28. RepresentativesPowermaps
29. Indirected
30. Powmap
31. ElementOrdersPowermap