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Groups with all proper subgroups nilpotent-by-finite rank

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Abstract.

In this paper the authors consider the class of groups in which every proper subgroup is nilpotent-by-finite rank. There exist infinite simple groups with this property. Among the results proved is the theorem that a locally soluble-by-finite such group that is not a perfect p-group is itself nilpotent-by-finite rank, provided the group has no infinite simple images.

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Authors and Affiliations

  1. Department of Mathematics, University of Alabama, Tuscaloosa, AL. 35487-0350, U.S.A., , , , , , US

    M. R. Dixon & M. J. Evans

  2. Department of Mathematics, Bucknell University, Lewisburg, PA. 17837, U.S.A., , , , , , US

    H. Smith

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  1. M. R. Dixon
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  2. M. J. Evans
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  3. H. Smith
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Received: 11.3.1999

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Dixon, M., Evans, M. & Smith, H. Groups with all proper subgroups nilpotent-by-finite rank. Arch. Math. 75, 81–91 (2000). https://doi.org/10.1007/PL00000436

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  • DOI: https://doi.org/10.1007/PL00000436

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