Make GroupElem broadcastable

[lgoettgens]

Replaces and thus closes https://github.com/oscar-system/Oscar.jl/pull/3787.

We already have the analogous thing for NCRingElem, so I see no reason not to have it for GroupElem.

cc @ThomasBreuer

[ThomasBreuer]

Thanks.

Then what about AbstractAlgebra.AdditiveGroupElem?

[lgoettgens]

Then what about AbstractAlgebra.AdditiveGroupElem?

There is no interface for AdditiveGroupElem defined at all here. Thus I would find it a bit weird to just add broadcastable and nothing else. Maybe @fingolfin or @thofma have some opinion on this?

[thofma]

This will clash with broadcasting of matrices.

[ThomasBreuer]

This will clash with broadcasting of matrices.

I had thought that such problems don't occur because we distinguish between matrices and matrix group elements.

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[thofma]

I had thought that such problems don't occur because we distinguish between matrices and matrix group elements.

This is true, but unrelated.

julia> x = ZZ[1 2; 3 4]
[1   2]
[3   4]

julia> x isa AbstractAlgebra.AdditiveGroupElem
true

[lgoettgens]

Thanks @thofma. So we should not add this for AdditiveGroupElem but only for FinGenAbGrpElem