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On Classes of Groups of Finite Metabelian Rank

Abstract

We introduce the notion of the metabelian rank of a group and study non-Abelian groups of finite metabelian rank. We prove the following result: If \(G \) is the extension of a locally finite group by a locally nilpotent-by-finite group and the metabelian rank of \(G \) is finite then the special rank of \(G \) is finite too.

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Correspondence to O. Yu. Dashkova.

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Dashkova, O.Y. On Classes of Groups of Finite Metabelian Rank. Sib. Adv. Math. 30, 192–199 (2020). https://doi.org/10.3103/S1055134420030049

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Keywords

  • special rank of a group
  • metabelian subgroup
  • locally finite group
  • locally nilpotent-by-finite group