Abstract
The finite p-groups such that, whenever H < G and \({|H|^{2}p < |G|}\), then \({H \triangleleft G}\), are classified. Nonnilpotent groups G such that, whenever H < G and \({|H|^{2}p < |G|}\), where p is a minimal prime divisor of \({|G|}\), then \({H \triangleleft G}\), are also classified. In this way we give an answer to Problems 1 and 7 posed in a paper of Y. Berkovich. By using generalizations of these problems we also obtain some new criteria for a group to be a solvable T-group.
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Malinowska, I.A. Finite groups all of whose small subgroups are pronormal. Acta Math. Hungar. 147, 324–337 (2015). https://doi.org/10.1007/s10474-015-0531-8
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DOI: https://doi.org/10.1007/s10474-015-0531-8