GroupGenerators

GroupGenerators[group]

returns a list of generators of group.

Details

  • The type of generators will depend on the representation type of the group.
  • For an explicit permutation representation, GroupGenerators[PermutationGroup[{g1,,gn}]] returns the list {g1,,gn}.
  • For a named abstract group, the generators of a default representation are returned.

Examples

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Basic Examples  (2)

Generators of a permutation group:

A symmetric group is generated by default with two permutations, a transposition, and a shift:

Scope  (3)

Generators for a group defined by generators:

Generators for a named group, using a default representation:

Support lengths of the default permutation generators of a sporadic simple group:

Introduced in 2010
 (8.0)