How to define subgroups of finitely presented groups in GAP?

Question

As an example, suppose I define D := DihedralGroup(8); I then use H := Image(IsomorphismFpGroup(D)); to get a finitely presented form of the group. GAP prints out the generators [F1,F2,F3]. Next I want to define the subgroup K := Subgroup(H, F2^2); After I enter this command I get an error

Error, Variable: 'F2' must have a value
not in any function at line 3 of *stdin*

Is there a correct way to define subgroups in GAP? I have noticed the subgroup command works for symmetric groups.

Answer 1

The following command should work:

K:=Subgroup(H,[H.2^2]);

Explanation:

• $\text{H.2}$ returns the second generator of $\text{H}$, which is the element $\text{F2}$ of $\text{H}$.$\\[2pt]$
• The first argument to the Subgroup command is the parent group.$\\[2pt]$
• The second argument to the Subgroup command is a list of generators, which explains the presence of the square brackets.