A subgroup H is said to be an s-permutable subgroup of a finite group G provided that the equality HP =PH holds for every Sylow subgroup P of G. Moreover, H is called SS-quasinormal in G if there exists a supplement B of H to G such that H permutes with every Sylow subgroup of B. We show that H is weakly SS-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable and H \ T is SS-quasinormal in G. We study the influence of some weakly SS-quasinormal minimal subgroups on the nilpotency of a finite group G. Numerous results known from the literature are unified and generalized.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 2, pp. 187–194, February, 2014.
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Zhao, T., Zhang, X. Weakly SS-Quasinormal Minimal Subgroups and the Nilpotency of a Finite Group. Ukr Math J 66, 209–217 (2014). https://doi.org/10.1007/s11253-014-0923-x
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DOI: https://doi.org/10.1007/s11253-014-0923-x