Abstract
According to Schmidt’s Theorem a finite group whose proper subgroups are all nilpotent (or a finite group without non-nilpotent proper subgroups) is solvable. In this paper we prove that every finite group with less than 22 non-nilpotent subgroups is solvable and that this estimate is sharp.
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Zarrin, M. A generalization of Schmidt’s Theorem on groups with all subgroups nilpotent. Arch. Math. 99, 201–206 (2012). https://doi.org/10.1007/s00013-012-0411-1
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DOI: https://doi.org/10.1007/s00013-012-0411-1