generators(FiniteGroupAction) -- generators of a finite group

Synopsis

• Function: generators

• Usage:

  generators G

• Inputs:
  • G, an instance of the type FiniteGroupAction, the action of a finite group
• Optional inputs:
  • CoefficientRing => ..., default value null,
• Outputs:
  • a list, a list of generators of the group

Description

Use this function to get the user-defined generators of a group action.

The following example defines the permutation action of a symmetric group on three elements using three transpositions.

i1 : R = QQ[x_1..x_3]

o1 = R

o1 : PolynomialRing

i2 : L = {matrix {{0,1,0},{1,0,0},{0,0,1}}, matrix {{0,0,1},{0,1,0},{1,0,0}}, matrix {{1,0,0},{0,0,1},{0,1,0}} }

o2 = {| 0 1 0 |, | 0 0 1 |, | 1 0 0 |}
      | 1 0 0 |  | 0 1 0 |  | 0 0 1 |
      | 0 0 1 |  | 1 0 0 |  | 0 1 0 |

o2 : List

i3 : G = finiteAction(L, R)

o3 = R <- {| 0 1 0 |, | 0 0 1 |, | 1 0 0 |}
           | 1 0 0 |  | 0 1 0 |  | 0 0 1 |
           | 0 0 1 |  | 1 0 0 |  | 0 1 0 |

o3 : FiniteGroupAction

i4 : generators G

o4 = {| 0 1 0 |, | 0 0 1 |, | 1 0 0 |}
      | 1 0 0 |  | 0 1 0 |  | 0 0 1 |
      | 0 0 1 |  | 1 0 0 |  | 0 1 0 |

o4 : List