Abstract.
We show that, for each finite group G, there exists an axiomatization of the class of abelian-by-G groups with a single sentence. In the proof, we use the definability of the subgroups M n in an abelian-by-finite group M, and the Auslander-Reiten sequences for modules over an Artin algebra.
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Received: 15 March 1996 / Published online: 18 July 2001
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Oger, F. Axiomatization of abelian-by-G groups for a finite group G. Arch. Math. Logic 40, 515–521 (2001). https://doi.org/10.1007/s001530100084
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DOI: https://doi.org/10.1007/s001530100084