obtain the generators of a group
obtain the generators of a group, with redundant ones filtered out
obtain labels for the generators of a group
group data structure
The Generators command returns a list of generators of a group.
The NonRedundantGenerators command returns a list of generators of a group, with redundant generators removed (no proper subset of the generators will generate the full group). This is typically a bit more time-consuming to compute than Generators.
The Labels command returns a list of labels for the generators of a group, or undefined if no labels are defined. In the first case, the labels are in the same order as the list that Generators returns.
g1 ≔ Group⁡a=Perm⁡1,2,b=Perm⁡2,3,Perm⁡3,4
Maple selects a label for the generator missing one.
In this case, none of the generators are labeled, so Maple does not select any labels.
g2 ≔ Group⁡1,2,2,3,3,4
Finitely presented groups use the names of the generators as labels.
g3 ≔ Group⁡a,b,a,a,b,b,a,b,a,b
A Cayley table groups returns all its elements as its list of generators.
g4 ≔ Group⁡1|2|3,2|3|1,3|1|2
g4≔ < a Cayley table group with 3 elements >
The GroupTheory[Generators], GroupTheory[NonRedundantGenerators] and GroupTheory[Labels] commands were introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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