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Permutation Groups
Changes:
- Constructions of PSO and POmega (and their plus/minus forms)
have been changed so that they return subgroups of the corresponding PGO.
- The ExtraSpecialGroup function now returns a minimal degree permutation
representation, rather than the regular representation previously returned.
- The FPGroup function has had restrictions on the group order lifted to 230 - 1,
equal to the current limit for the degree of a permutation group.
New Features:
- The test for maximality of a subgroup of a permutation group now uses an
algorithm which exploits Magma's ability to construct maximal subgroups in large groups.
- Blocks action code has been modernised, along with use of the minimal block
finder, to make better use of the fast minimal blocks algorithm.
This has impacted important routines such as finding the soluble radical
and Sylow subgroups, the basic test IsAltsym, and degree reduction code.
Dealing with high degree transitive and imprimitive groups, such as are
produced from fp-groups using the Todd-Coxeter, has been much improved.
- Testing for regular groups has been modernised, and more use is made of the
regularity property, particularly when the group order or a presentation is
required.
- A new operation on permutations has been installed: TensorProduct.
This is equivalent to converting the two permutations to matrices, taking tensor
product of matrices, and converting back to a permutation, but without making a matrix.
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