RightCosetRepresentative

RightCosetRepresentative[group,g]

returns the smallest element in the right coset of products of the elements of group by g.

Details and Options

  • The representative is chosen as the smallest element in the coset, as determined by the ordering given by Less.

Examples

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Basic Examples  (2)

Representative of a coset:

For an element in the group, the representative is the identity:

Scope  (1)

Compute the canonical representative of a right coset:

List all elements of the corresponding right coset:

The smallest element is the canonical representative:

Properties & Relations  (1)

The inverse of the canonical representative of a right coset belongs to the left coset but is not canonical in general. Take a permutation and a group:

This is the left coset of the inverse of that element:

The inverse of the canonical right coset representative belongs to the coset but is not the canonical representative:

Introduced in 2010
 (8.0)