Dear Forum,

Barry Monson wrote:

Suppose G is a permutation group, say with
generators, a,b,c, and with some subgroup
H. How can I get permutations representing the
action of G on the right cosets of H?
I realize this must be a trivial command or two,
but somehow I cannot make Gap do the job.

You want to use `Action' (to get an image group) or `ActionHomomorphism' (to
get a homomorphism to a permutation group). Thus

Action(G,RightCosets(G,H),OnRight);

In fact (since this is such a prominent task) there is a better performing
version, that acts only on representatives of the cosets:

Action(G,RightTransversal(G,H),OnRight);

Best wishes,

Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, Fort Collins, CO 80523, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke