ApproximateKernel( G, P, m, n [,maps] )
G is an irreducible matrix group. P is a permutation representation of G.
ApproximateKernel returns a generating set for a subgroup of the
kernel of a homomorphism from G to P. The parameter m is the
maximum number of random relations constructed in order to obtain
elements of the kernel. If n successive relations provide no new
elements of the kernel, then we terminate the construction. These two
parameters determine the time taken to construct the kernel; n can be
used to increase the probability that the whole of the kernel is
constructed. The suggested values of m and n are 100 and 30,
respectively.
Assume that G has r generators and P has s generators. The optional argument maps is a list of length r containing integers between 0 and s. We use maps to specify the correspondence between the generators of G and the generators of P. An entry 0 in position i indicates that G.i maps to the identity of P; an entry j in position i indicates that G.i maps to P.j. By default, we assume that G.i maps to P.i.
The function is similar to RecogniseMatrixGroup but here we already
know .quotient is G and we have a permutation representation P for
G. The function returns a record containing information about the
kernel. The record contents can be viewed using DisplayMatRecord.
The algorithm is described in [13]; the implementation is currently experimental.
GAP 3.4.4