Extensions

[fingolfin]

I am wondering in how far this should be left at the "core" API, or whether we should also start to define a few more things? E.g.

• basic properties like isabelian, issolvable, isnilpotent, isperfect...
• standard subgroups like derivedsubgroup(G), center(G), socle(G), ... or sylowsubgroup(G, p)
• some subgroup related functionality like issubgroup(A,B), isnormalsubgroup(A,B), ...
• standard operations like centralizer(G, H), normalizer(G, H), normalizer(G, H), ...

[albinahlback]

I think this sounds very nice, great examples! Not familiar with everything, but I do think that general group-things would fit the package.

[fingolfin]

There are many more, of course, e.g.

• trivial_subgroup
• istrivial (default implementation could be istrivial(G) = isfinite(G) && order(G) == 1)
• issupersolvable
• iscyclic
• issimple

Basically one can take a look at https://www.gap-system.org/Manuals/doc/ref/chap39.html and add things from there, including reusing some of the documentation. I am not sure whether it makes sense to do that here, though, as we wouldn't be providing implementations for most. I am happy to just have these all in Oscar.jl, and only move things to the "core" which others find interesting.

[fingolfin]

I think the two main piece of infrastructure still missing are handling of subgroups; and homomorphisms. All the other things are sugar on top; but subgroups are a central thing and not yet covered by GroupsCore at all, as far as I can tell.

[albinahlback]

Good thinking!

I think me and @kalmarek had a discussion that there is nothing stopping some extending package to implement subgroups on their own, since I tried to do something like

operation(g::GroupElement, h::GroupElement)

which I (after this discussion) think is too general.

Continuing along the lines with your comment, I think it would be natural to extend our current interface to something like

operation(g::GEl, h::GEl) where {GEl <: GroupElement}
operation(g::GEl, h::HEl) where {GEl <: GroupElement, HEl <: GroupElement}

where the parent of elements in HEl must either be a subgroup or supergroup of the parent of elements in GEl.

[fingolfin]

I don't understand your last comment, @albinahlback . What ist operation and what does it have to do with subgroups?

[albinahlback]

Sorry for being unclear, don't mind what I said.

Do you think we should define an abstract type called Subgroup, or do you have a vision of something else, @fingolfin?

[kalmarek]

@fingolfin If you wish to discuss subgroups and homomorphisms, I'm all ears. ping me on slack