The centralizer of an element a of a magma m is the set of all members of m that commute with a.

The Centralizer command returns the centralizer in m of the element a, as a set.

The Centraliser command is provided as an alias.

$\mathrm{with}\left(\mathrm{Magma}\right)\:$

$m≔⟨⟨⟨1\|2\|3\|4\|5\|6⟩\,⟨2\|1\|6\|5\|4\|3⟩\,⟨3\|5\|1\|6\|2\|4⟩\,⟨4\|6\|5\|1\|3\|2⟩\,⟨5\|3\|4\|2\|6\|1⟩\,⟨6\|4\|2\|3\|1\|5⟩⟩⟩$

$m≔\left[\begin{array}{cccccc}1& 2& 3& 4& 5& 6\\ 2& 1& 6& 5& 4& 3\\ 3& 5& 1& 6& 2& 4\\ 4& 6& 5& 1& 3& 2\\ 5& 3& 4& 2& 6& 1\\ 6& 4& 2& 3& 1& 5\end{array}\right]$

$\mathrm{Centralizer}\left(2\,m\right)$

$\left\{1\,2\right\}$

The Magma[Centralizer] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.