PcGroups as FPGroups

[fieker]

To me, pc-groups are clearly fp-groups (in fact they are better, but at least they are fp). Thus I'd like to use the fp-interface (relations e.g.)...

How?

Related: turn pc into perm?

[fingolfin]

Try isomorphic_fp_group and friends. Alternative ways to deal with this welcome.

We could also add a relators methods for pc groups but it'd be essentially implemented as g -> relators(isomorphic_fp_group(g))

[fingolfin]

("Alternatives" as in: other interfaces you'd expect)

[fingolfin]

Based on discussion with @fieker , we need wrappers for at least these GAP functions:

• IsomorphismFpGroupByPcgs
• IsomorphismFpGroupByGenerators
• IsomorphismRefinedPcGroup
• perhaps also IsomorphismSpecialPcGroup

[fingolfin]

There are two dual ways to approach this:

• one is to provide more and better ways to compute isomorphisms between any kinds of group and in particular with certain prescribed generators; that's what IsomorphismFpGroupByPcgs and IsomorphismFpGroupByGenerators
• or one could have more interfaces that are shared between fp groups and pc groups, such as relators for both of those. But then it would be important to state what properties these common interfaces should satisfy to be actually useful.

Esp. for the second point we should look at e.g. PR #985 to see how that code uses e.g. relators resp. to study the code duplication there between pc groups and fp groups code, and come up with ways to reduce it.

[ThomasBreuer]

Concerning @fieker's question

Related: turn pc into perm?

Apparently GAP offers currently only the right regular permutation action.

[fingolfin]

Also we have isomorphic_perm_group