Axiomatization of abelian-by- G groups for a finite group G

Archive for Mathematical Logic 40 (7):515-521 (2001)
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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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10.1007/s001530100084

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Citations of this work

Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups.Francis Oger - 2001 - Journal of Symbolic Logic 66 (3):1471-1480.

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On the definability of verbal subgroups.Françcoise Point - 2001 - Archive for Mathematical Logic 40 (7):525-529.

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