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Elementary equivalence and genus of finitely generated nilpotent groups
Published online by Cambridge University Press: 17 April 2009
Abstract
We show that, if two finitely generated nilpotent groups are elementarily equivalent, and more generally if they satisfy the same sentences with one alternation of quantifiers, then, they are quite similar, though not necessarily isomorphic. For instance, each of them is isomorphic to a subgroup of finite index of the other and they have the same finite images, the same Mislin genus and the same Pickel genus.
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- Copyright © Australian Mathematical Society 1988
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