construct the commuting graph of a group
CommutingGraph( G )
CommutingGraph( G, elements = E )
a small group
(optional) list, set, or one of the names all or noncentral
elements = list, set, or one of the names all or noncentral
Specifies a selection of the elements of G to include as vertices of the generated graph.
If elements is a list or set, these elements are included.
If elements is noncentral, all elements of G except central elements are included.
If elements is all (the default), all elements of G are included.
For a finite group G and a subset E of its elements, the commuting graph of G and E is the graph whose vertices are elements of E and for which two vertices p and q are adjacent if pq=qp in G.
The CommutingGraph( G ) command returns the commuting graph of G.
You can specify a particular ordering for the elements of the group by passing the optional argument elements = E, where E is an explicit list of the members of G.
Note that computing the commuting graph of a group requires that all the group elements be computed explicitly, so the command should only be used for groups of modest size.
Draw the commuting graph of the symmetric group of degree 4.
G ≔ SymmetricGroup⁡4
Draw the commuting graph of the dihedral group of degree 7.
G ≔ DihedralGroup⁡7
Draw the commuting graph of a Frobenius group of order 72.
G ≔ FrobeniusGroup⁡72,1
G≔ < a permutation group on 9 letters with 5 generators >
The GroupTheory[CommutingGraph] command was introduced in Maple 2023.
For more information on Maple 2023 changes, see Updates in Maple 2023.
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