factor a group element into a subgroup element and a coset representative
Factor( g, H )
permutation or word on the generators of the supergroup of H
a permutation group or a subgroup of a finitely presented group
Let H be a subgroup of a group G, and let g be a member of G. Let R be a complete set of representatives of the right cosets of H in G. Then g can be written, uniquely, in the form g=h·r, with h in H and r in R.
The Factor( g, H ) command returns a pair [ h, r ], where h belongs to H, and r is a coset representative for the coset H.g in a supergroup of H.
If H is a permutation group, then the representative is for the cosets of H in the full symmetric group of the same degree as H. If H is a subgroup of a finitely presented group G, then the representative r is for the cosets of H in G.
The set of representatives used is the set obtained from the RightCosets command applied to H.
First we consider the following subgroup of the symmetric group of degree 7.
We can factor this permutation over the cosets of H in Symm(7).
Next, consider the group of the (2,3)-torus knot, which is an infinite group.
The following subgroup of G has index in G equal to 3.
The alternating group of degree 5 has the following presentation.
The GroupTheory[Factor] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
Download Help Document
What kind of issue would you like to report? (Optional)