Dear GAP Forum

Laurent Bartholdi wrote:

hello world,
i run into a problem with gap, which is:

G := FreeGroup("a","b","c","d");
ga := G.1; gb := G.2; gc := G.3; gd := G.4;
H := Subgroup(G,[ga^2,gb,gc,gd,gb^ga,gc^ga,gd^ga]);
phi := [GroupHomomorphismByImages(H,G,[ga^2,gb,gc,gd,gb^ga,gc^ga,gd^ga],
[Identity(G),ga,ga,Identity(G),gc,gd,gb]);

ap> Image(phi,H.1);
<identity ...>
[this is ok]
gap> Image(phi,H.1^2);
[endless loop, instead of <identity ...>]
gap> Image(phi,H.1*H.3);
fail
[instead of a]

That's a coincidence. That is exactly the same problem that I mentioned in
my message to the Forum yesterday.

As you say, the fact that the procedure to express an element in terms of
subgroup generators is difficult in general, is no reason not to provide
methods for doing this when the index is small!

Derek Holt.