On the undecidability of some classes of abelian-by-finite groups

Annals of Pure and Applied Logic 62 (2):167-173 (1993)
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Abstract

Let G be a finite group. For every formula ø in the language of groups, let K denote the class of groups H such that ø is a normal abelian subgroup of H and the quotient group H;ø is isomorphic to G. We show that if G is nilpotent and its order is not square-free, then there exists a formula ø such that the theory of K is undecidable

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