#### Some further generators

Given a permutation *g*, a group isomorphic to the
centralizer of *g* can be computed by

INT gen_centralizer_permutation(a,b) OP a,b;

Since we do not compute the centralizer of *g*, but a group
isomorphic to this centralizer, we input the cycle type
of *g* (as a PARTITION of type EXPONENT) as `a`

.
`b`

becomes a system of generators of a group
isomorphic to the centralizer of *g*, computed by
a formula from [11].
The generators of a group isomorphic to the stabilizer
of a partition can be computed by

INT gen_stabilizer_partition(a,b) OP a,b;

`a`

is a PARTITION object of type EXPONENT.
`b`

is the computed system of generators.
Using the routine

INT gen_young_partition(a,b) OP a,b;

you can compute a VECTOR of generators of Young groups.
To a given PARTITION `a`

(of type EXPONENT or VECTOR)
generators of the corresponding Young group are computed in `b`

.
There are some further routines which read certain systems
of generators from data files. In order to work with
these files you must have the corresponding data files
in a subdirectory of the working directory called "data".

INT gen_M24(a) OP a;

reads a system of generators of the Mathieu group M24 from the
file `m24.gen`

.
In the same way generators of fullerenes
can be handled in SYMMETRICA.

harald.fripertinger@kfunigraz.ac.at,

last changed: November 19, 2001