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.

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

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

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

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

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

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

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