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GroupCentralizer[group,g]

returns the centralizer of the element g in group.

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GroupCentralizer

GroupCentralizer[group,g]

returns the centralizer of the element g in group.

Details

  • The centralizer of an element g in group is the subgroup of elements of group that commute with g.

Examples

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Basic Examples  (1)

Take a permutation group:

And a permutation:

This is the subgroup of permutations in the group that commutes with the permutation g:

Scope  (1)

Take a permutation group:

And a permutation:

This is the subgroup of permutations in the group that commutes with the permutation g:

Check the result by direct computation of products with all elements:

This function checks that a permutation h commutes with g:

All 16 permutations in the centralizer commute with g:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_groupcentralizer, author="Wolfram Research", title="{GroupCentralizer}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/GroupCentralizer.html}", note=[Accessed: 18-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_groupcentralizer, organization={Wolfram Research}, title={GroupCentralizer}, year={2010}, url={https://reference.wolfram.com/language/ref/GroupCentralizer.html}, note=[Accessed: 18-August-2025]}