Abstract
Given a finite groupG andp an odd prime number, we conclude thatO p(G)∩G′ isp-nilpotent when for every subgroupH ofG of orderp there exists a subgroupK ofG such thatG=HK andH permutes with every subgroup ofK.
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Carocca, A. A note on a theorem of W. Gaschütz and N. Itô. Bol. Soc. Bras. Mat 26, 161–165 (1995). https://doi.org/10.1007/BF01236991
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DOI: https://doi.org/10.1007/BF01236991