Primitivity testing of finite nilpotent linear groups
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Rossmann, Tobias (2011). Primitivity testing of finite nilpotent linear groups. LMS Journal of Computation and Mathematics 14 , 87-98
We describe a practical algorithm for primitivity testing of finite nilpotent linear groups over various fields of characteristic zero, including number fields and rational function fields over number fields. For an imprimitive group, a system of imprimitivity can be constructed. An implementation of the algorithm in MAGMA is publicly available.