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The author would like to thank O. H. Kegel and the refree for warm help and useful advice.
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Xu, M. Groups whose proper subgroups are finite-by-nilpotent. Arch. Math 66, 353–359 (1996). https://doi.org/10.1007/BF01781552
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DOI: https://doi.org/10.1007/BF01781552