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GAP Fusion Systems

A GAP package that implements core operations on fusion systems.

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Some suggestions

I stumbled over this repository by chance and have some feedback:

  • don't use the AllGroups name, it is obsolete and deprecated; use AllSmallGroups
  • this command can take filters, which is often more efficient than first constructing all groups and then filtering. E.g. AllSmallGroups(n, IsAbelian, false) to get only non-abelian groups
  • avoid AllSubgroups if you can, in many applications it is sufficient (and much more efficient) to work with ConjugacyClassesSubgroups
  • StructureDescription is a toy for interactive use. Its output can change at any time. So don't use checks like StructureDescription(P) <> "C4"
  • GAP already has a command to compute O_p(G), namely PCore(G, p)
  • replace ConjugationHomomorphism(H, H, g) by GAP's ConjugatorAutomorphism for which various things will be more efficient (there is also ConjugatorIsomorphism for the general case where domain/source and codomain/range disagree, if you need it; read the docs to find out details; )
  • instead of hard coding limits to decide whether IdGroup is available, maybe better to use IdGroupsAvailable

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