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New features:
-
The function IsTensorInduced has been introduced which
decides whether or not a matrix group is tensor-induced.
It replaces and upgrades IsSymmetricTensorProduct which
has been withdrawn.
The related functions SymmetricTensorBasis and
SymmetricTensorPermutations have been renamed
TensorInducedBasis and TensorInducedPermutations respectively.
- An optional argument has been added to IsPrimitive
which allows one to search for certain block sizes only;
a similar argument added to IsTensor allows one to
search for factors of particular dimensions.
- The function OrbitsOfSpaces(G, k) has been introduced which
constructs lengths and orbit representatives for the k-dimensional
spaces of the natural vector space under action of G, a matrix
group defined over a prime field.
- The function NumberOfFixedSpaces(g, k) has been introduced which
determines the number of k-dimensional subspaces of the
natural vector space fixed under the action of
.
- The function StabiliserOfSpaces has been introduced which
constructs the subgroup of GL(d, q) which stabilises a sequence of
subspaces of the natural vector space.
- The function EstimateOrbit(G, U), which
estimates the size of the orbit of the subspace U under action of G,
has been introduced.
- The function ApproximateStabiliser(G, A, U) has been introduced
which constructs, using a random approach, a subgroup of the stabiliser
of the subspace U under the induced action A of G.
- The permitted arguments to ExteriorSquare now include
a matrix group.
-
The database of irreducible soluble groups has been converted
into a new style database.
Next: Finitely Presented Groups [HB
Up: Groups
Previous: General Matrix Groups [HB