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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Group Theory > GroupCentralizer >

BUILT-IN MATHEMATICA SYMBOL

GroupCentralizer

returns the centralizer of the element g in group.

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

Take a permutation group:

And a permutation:

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

Take a permutation group:

Out[1]=

And a permutation:

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

Out[3]=

Out[4]=

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: