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-dimensionalpl -manifold with zero Euler characteristic in terms of the Reidemeister torsion of this manifold.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 66, pp. 204–205, 1976.