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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

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