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Preprint Number 622
622. Clément Lasserre and Francis Oger Direct products and elementary equivalence of polycyclic-by-finite
groups E-mail: Submission date: 10 September 2013. Abstract: We give an algebraic characterization of elementary equivalence for
polycyclic-by-finite groups. Using this characterization, we investigate the
relations between their elementary equivalence and the elementary
equivalence
of the factors in their decompositions in direct products of indecomposable
groups. In particular we prove that the elementary equivalence of two such
groups G,H is equivalent to each of the following properties: It is not presently known if 1) implies elementary equivalence for any groups G,H. Mathematics Subject Classification: 20A15 (20F22) Keywords and phrases: |

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