   Generators of permutation groups

#### Generators of permutation groups

A system of generators of a permutation group in SYMMETRICA is considered to be a VECTOR, where each entry of this VECTOR is a PERMUTATION object (in VECTOR-form), all of the same degree.

In order to compute a system of generators for some standard actions you can use

```INT gen_Cn(a,b)    OP a,b;
INT gen_Dn(a,b)    OP a,b;
INT gen_An(a,b)    OP a,b;
INT gen_An_3(a,b)  OP a,b;
INT gen_Sn(a,b)    OP a,b;
INT gen_In(a,b)    OP a,b;
```
As their names imply one can compute the generators of the natural actions of the cyclic group `Cn`, the dihedral group `Dn`, the alternating group `An`, the symmetric group `Sn` and the trivial group consisting of the identity only `In` respectively. In `gen_An_3` the set of all cycles of length 3 is computed as the system of generators of the alternating group. In all these cases `a` is the degree of the permutation group (i.e. the number of elements of the set which the group is acting on). `b` is the VECTOR of generators. `a` and `b` must be different.

There is another routine called

```INT gen_arb(a)      OP a;
```
which serves as an input routine for `a`, an arbitrary system of generators.
harald.fripertinger@kfunigraz.ac.at,
last changed: November 19, 2001   Generators of permutation groups