IsIrreducibleFiniteNilpotent(G : parameters): GrpMat -> BoolElt, Any

    DecideOnly: BoolElt                 Default: false

    Verify: BoolElt                     Default: false

Let G be a finite nilpotent matrix group over K, where K is a number field or a rational function field over a number field. The function returns true if G is irreducible or false and a proper submodule of GModule(G). The construction of a submodule can be suppressed by setting DecideOnly to true. If Verify is set to true, then the function checks if G is nilpotent and finite. The algorithm used for irreducibility testing is described in [Ros10a].

IsPrimitiveFiniteNilpotent(G : parameters): GrpMat -> BoolElt, Any

    DecideOnly: BoolElt                 Default: false

    Verify: BoolElt                     Default: false

Let G be an irreducible finite nilpotent matrix group over K, where K is a number field or a rational function field over a number field. The function returns true if G is primitive or false and a a system of imprimitivity for G, given as a sequence of subspaces of RSpace(G). The construction of a system of imprimitivity can be suppressed by setting DecideOnly to true. If Verify is set to true, then the function checks if G is nilpotent, finite, and irreducible. The algorithm used for primitivity testing is described in [Ros10b].

References

[Ros10a] T. Rossmann. Irreducibility testing of finite nilpotent linear groups. J. Algebra 324(5): 1114-1124, 2010.

[Ros10b] T. Rossmann. Primitivity testing of finite nilpotent linear groups. Submitted.