Dear GAP-Forum,
Anton Konygin wrote:
Let G be a group generated by permutations g_1, ..., g_d on the set
{1,
..., n} and H be a subgroup of G generated by permutations
h_1, ..., h_k
on the set {1, ..., n} (g_1, ..., g_d, h_1, ..., h_k are given
explicitly).
Can I use GAP to get the natural (permutation) action of g_1, ...,
g_d on
left cosets of G by H (ordering in some way)?
GAP uses right cosets and action from the right:
A:=Action(G,RightTransversal(G,H),OnRight);
Then
GeneratorsOfGroup(A) give the action of g1,..g_d.
(To get the (left) action on the left cosets, you would have to
simply invert the permutations.)
If you want the homomorphism, you can use
phi:=ActionHomomorphism(G,RightTransversal(G,H),OnRight);
Best wishes,
Alexander Hulpke
_______________________________________________
Forum mailing list
[email protected]
http://mail.gap-system.org/mailman/listinfo/forum
