abelian_group

[fieker]

julia> abelian_group(PcGroup, [8])
ERROR: cannot create a PcGroup group with relative orders [8], perhaps try SubPcGroup
Stacktrace:
 [1] error(s::String)

but

pc_group(abelian_group([8]))

[lgoettgens]

@ThomasBreuer can you have a look at this?

[ThomasBreuer]

Yes.
The point is that abelian_group(PcGroup, [8]) would have to create a PcGroup whose generators correspond to the given element orders, in this case [8]; GAP's PcGroup objects do not allow this, the cyclic pc group of order 8 would have three generators.
On the other hand, abelian_group([8]) returns a FinGenAbGroup, and pc_group then creates a group with 3 generators.

[ThomasBreuer]

Ah, and concerning the obvious question why abelian_group(PcGroup, [8]) does not create an Oscar group with only one generators such that the underlying GAP group may have three generators:
There was also the general requirement that the gens value of pc groups and fp groups correspond to the generators of the defining presentation.

[thofma]

I remember vaguely that we agreed on abelian_group(T, [...]) should have generators of the right order etc, but I can't find it written down anymore. Given this, I think everything is working as expected.

[ThomasBreuer]

@thofma The documentation of abelian_group says

The gens value of the returned group corresponds to v, that is, the number
of generators is equal to length(v) and the order of the i-th generator is
v[i].

And the documentation of PcGroup says

For a group G of type PcGroup, the elements in gens(G) satisfy the relators
of the underlying presentation.