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Commensurability and elementary equivalence of polycyclic groups

Published online by Cambridge University Press:  17 April 2009

Deborah Raphael
Deborah Raphael
Affiliation:
Universidade de Sāo PauloInstituto de Matemática e EstatísticaCaixa Postal 66281 – CEP 05389–970Sāo Paulo – Brasil
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Abstract

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It is shown that two polycyclic-by-finite groups G and H, satisfying the same sentences with one alternation of quantifiers, are commensurable. In fact we show something stronger: given n > 1 there is a subgroup Hn of H and a subgroup Gn of G such that Hn≃G, Gn≃H and the indices [G: Gn] and [H: Hn] are finite and prime to n.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 3 , June 1996 , pp. 425 - 439
Copyright
Copyright © Australian Mathematical Society 1996

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