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Magma

 Centralizer
 compute the centralizer of a magma

 Calling Sequence Centralizer( a, m ) Centraliser( a, m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Magma}\right):$
 > $m≔⟨⟨⟨1|2|3|4|5|6⟩,⟨2|1|6|5|4|3⟩,⟨3|5|1|6|2|4⟩,⟨4|6|5|1|3|2⟩,⟨5|3|4|2|6|1⟩,⟨6|4|2|3|1|5⟩⟩⟩$
 ${m}{≔}\left[\begin{array}{cccccc}{1}& {2}& {3}& {4}& {5}& {6}\\ {2}& {1}& {6}& {5}& {4}& {3}\\ {3}& {5}& {1}& {6}& {2}& {4}\\ {4}& {6}& {5}& {1}& {3}& {2}\\ {5}& {3}& {4}& {2}& {6}& {1}\\ {6}& {4}& {2}& {3}& {1}& {5}\end{array}\right]$ (1)
 > $\mathrm{Centralizer}\left(2,m\right)$
 $\left\{{1}{,}{2}\right\}$ (2)

Compatibility

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