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Commensurability and elementary equivalence of polycyclic groups
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1996
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