[GAP Forum] How do I construct the rank 2 free metabelian group of exponent n?

[Will Chen]

Let [image: F] be the free group in two generators [image: x,y], and [image:
n] an integer. I would like to create the group [image: F/F''F^n]. This is
a finitely generated solvable group of exponent [image: n], and hence is
finite.

Unfortunately, the subgroups [image: F'',F^n] are infinitely generated.
Creating [image: F'] via "DerivedSubgroup(F)" seems to work, since [image:
F] is finitely generated, but creating [image: F''] by calling
"DerivedSubgroup" doesn't seem to halt.

Also, I don't know of a command that can create [image: F^n].

Is it possible to construct the finite group [image: F/F''F^n] in GAP?

- Will