Cayley graph of an infinite group using GAP

Question

I have a finitely presented group which is infinite, and I wish to create a visual representation of its Cayley graph using GAP.

If possible I would like to do this using YAGS package.

My group is $\langle a, b\mid a^3 = b^3 = (ab)^3 = e\rangle$.

Its easy to define it in GAP, but it is infinite and for a visualization I should somehow choose only finitely many of its elements.

I'm looking for something like this:

Answer 1

You can use Bartholdi's package FR:

gap> LoadPackage("FR");

gap> f := FreeGroup( "a", "b" );;

gap> g := f / [ f.1^3, f.2^3, (f.1*f.2)^3 ];
<fp group on the generators [ a, b ]>

gap> WordGrowth(g,rec(limit:=4,draw:="Cayley.dot"));

this returns a dot file which you can open with e.g. imagemagick or convert to another format. DOT is a widely used format for graph so you'll find tool if the layout doesn't suits you.

$F_2/ {a^3 ; b^3 ; (ab)^3}$}" />