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Matrix Groups Over Finite Fields
The following notes describe new features that have been developed for use
in the context of the Composition Tree representation of a matrix group.
New Features:
- Short presentations on standard generators for the orthogonal groups
have been installed. The availability of presentations enables rapid
verification of the Composition Tree for any group whose composition
factors exclude exceptional groups of Lie type.
- The intrinsic ClassicalRewrite writes an element of a classical
group G
as an SLP in the standard generators of G
.
- Lifting-style algorithms have been implemented by Derek Holt for further
types of structural calculations in matrix groups using the Composition
Tree data structure.
These include LMGCentraliser, LMGIsConjugate (for elements),
LMGConjugacyClasses, LMGNormaliser, LMGIsConjugate
(for subgroups) and
LMGMaximalSubgroups. In the near future, each intrinsic prefixed with
the letters ``LMG'' will be merged with the corresponding standard intrinsic.
- A new intrinsic AffineGroup takes a matrix group G
over a
finite field and returns the semidirect product of G
by the natural
G
-module as a permutation group where the degree is the size of the
natural module.
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