GroupElementPosition

GroupElementPosition[group,g]

returns the position of the element g in the list of elements of group.

GroupElementPosition[group,{g1,,gn}]

returns the list of positions of the elements g1,,gn in group.

Details and Options

  • Each position is an integer between 1 and the order of the group.
  • The positions of elements in a permutation group are by default based on the standard ordering of their images.
  • The ordering of elements in a permutation group can be controlled by setting the GroupActionBase option.

Examples

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Basic Examples  (1)

Find positions of group elements in a group. The identity is always the first element:

Scope  (2)

Position of a permutation in the list of elements of a group:

List of positions of several elements in a group:

Options  (1)

GroupActionBase  (1)

Change the ordering of the permutations in a group by specifying a base:

Properties & Relations  (1)

GroupElements performs the inverse operation for a list of elements:

Possible Issues  (1)

For an element not present in the group the input is returned unevaluated:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2021_groupelementposition, author="Wolfram Research", title="{GroupElementPosition}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/GroupElementPosition.html}", note=[Accessed: 19-January-2022 ]}

BibLaTeX

@online{reference.wolfram_2021_groupelementposition, organization={Wolfram Research}, title={GroupElementPosition}, year={2010}, url={https://reference.wolfram.com/language/ref/GroupElementPosition.html}, note=[Accessed: 19-January-2022 ]}