Abstract
It is proved that if \(G\) is a strongly locally graded group of infinite rank whose proper subgroups of infinite rank are (locally finite)-by-nilpotent, then \(G\) itself is (locally finite)-by-nilpotent. A corresponding result is also obtained for groups whose proper subgroups of infinite rank are (locally finite)-by-(locally nilpotent).
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This work was partially supported by a research project of the “Dipartimento di Matematica e Applicazioni R. Caccioppoli” (Strutture Algebriche, Strutture Geometriche e Metodologie Didattiche)—The first author is a member of GNSAGA (INdAM).
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de Giovanni, F., Trombetti, M. Groups of infinite rank with a locally finite term in the lower central series. Beitr Algebra Geom 56, 735–741 (2015). https://doi.org/10.1007/s13366-014-0207-5
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DOI: https://doi.org/10.1007/s13366-014-0207-5