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

open allclose all

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:

Wolfram Research (2010), RightCosetRepresentative, Wolfram Language function, https://reference.wolfram.com/language/ref/RightCosetRepresentative.html.

Text

Wolfram Research (2010), RightCosetRepresentative, Wolfram Language function, https://reference.wolfram.com/language/ref/RightCosetRepresentative.html.

CMS

Wolfram Language. 2010. "RightCosetRepresentative." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RightCosetRepresentative.html.

APA

Wolfram Language. (2010). RightCosetRepresentative. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RightCosetRepresentative.html

BibTeX

@misc{reference.wolfram_2024_rightcosetrepresentative, author="Wolfram Research", title="{RightCosetRepresentative}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/RightCosetRepresentative.html}", note=[Accessed: 21-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_rightcosetrepresentative, organization={Wolfram Research}, title={RightCosetRepresentative}, year={2010}, url={https://reference.wolfram.com/language/ref/RightCosetRepresentative.html}, note=[Accessed: 21-November-2024 ]}