Ad hoc Magma code
- Magma code and documentation for simple extensions of reflection subgroups of unitary reflection groups for the paper: Reflection subgroups of finite complex reflection groups, J. Algebra 366, 218–234 (2012)
- Magma code and documentation for complements of a parabolic subgroup of a unitary reflection group in its normalise for the paper: Normalisers of parabolic subgroups in finite unitary reflection groups, J. Algebra 504, 479–505 (2018)
Conjugacy classes in finite classical groups
The conjugacy classes of classical groups are parametrized by invariants, which in most cases can be computed rapidly. The Magma code documented here finds the conjugacy classes by first computing the invariants then finding a representative matrix for each invariant.
On invoking Classes(G) for a classical group G, Magma first attempts to compute the classes via invariants and if this is not possible it falls back to other (more time-consuming) methods.
- Symplectic groups Sp(2n,q), the conformal symplectic groups CSp(2n,q) and all groups between these, provided q is a power of an odd prime.
- General orthogonal groups GO(2n+1,q), GO+(2n,q) and GO–(2n,q), provided q is a power of an odd prime. Magma also contains code to compute conjugacy classes in the conformal orthogonal groups.
- Unitary groups GU(n,q), the special unitary groups SU(n,q) and all groups between, for all prime powers q.
This package illustrates the construction of user-defined types in Magma.
A nearfield satisfies all the axioms of a field except for the commutative law of multiplication and one of the distributive laws. The Magma code implements right-distributive nearfields.