| | | **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** |