Reidemeister torsion and group invariants of three-dimensional manifolds

Two formulas are presented in this note. The first is purely algebraic and expresses the first elementary ideal of a finitely generated group in terms of the module of elementary derivatives. The second formula expresses the module of elementary derivatives of the fundamental group of a connected compact three-dimensional $pl$-manifold with zero Euler characteristic in terms of the Reidemeister torsion of this manifold.