# numgens(FiniteGroupAction) -- number of generators of a finite group

## Synopsis

• Function: numgens
• Usage:
numgens G
• Inputs:
• Outputs:
• an integer, the number of generators of the group

## Description

This function is provided by the package InvariantRing.

Use this function to get the number of 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 : numgens G o4 = 3

## Caveat

The integer returned by this function is not necessarily the minimal number of generators of the group, rather it is the cardinality of the generating set defined by the user.