We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group G is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of G. We also provide a simple new algorithm for integrality testing of finitely generated solvable-by-finite linear groups over the rational field. The algorithms have been implemented in Magma.
|Number of pages||8|
|Journal||Journal of Symbolic Computation|
|Issue number||Part 1|
|Early online date||11 Aug 2014|
|Publication status||Published - 1 May 2015|