Let H be a subgroup of a group G. We say that H satisfies Π-property in G if |G/K: NG/K(HK/K ∩ L/K)| is a π(HK/K ∩ L/K)-number for any chief factor L/K of G. If there is a subnormal supplement T of H in G such that H ∩ T ≤ I ≤ H for some subgroup I satisfying Π-property in G, then H is said to be Π-normal in G. Using these properties that hold for some subgroups, we derive new p-nilpotency criteria for finite groups.
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∗Supported by the NNSF of China, grant No. 11471055.
Translated from Algebra i Logika, Vol. 54, No. 3, pp. 326-350, May-June, 2015.
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Li, B., Foguel, T. On Π-Property and Π-Normality of Subgroups of Finite Groups. II. Algebra Logic 54, 211–225 (2015). https://doi.org/10.1007/s10469-015-9342-9
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DOI: https://doi.org/10.1007/s10469-015-9342-9