Abstract
Let Δ be a field of fractions of a torsion free nilpotent group ring KG, and D k× k a matrix subring of Δ n× n . We prove that if the field D has dimension m 2 over its center, then ( km)∣ n. The result remains true when G is residually torsion free nilpotent and Δ is the subfield of the Malcev-Neumann power series ring K 〈 G 〉, generated by KG.
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