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Weakly C*-Normal Subgroups and p-Nilpotency of Finite Groups

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Author(s): Shitian Liu

Journal: Asian Journal of Algebra
ISSN 1994-540X

Volume: 2;
Issue: 1;
Start page: 17;
Date: 2009;
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Keywords: Sylow p-subgroups | weakly c*-normal subgroups p-nilpotent | minimal subgroup

ABSTRACT
A subgroup H is called to be weakly c*-normal in G if there exists a subnormal subgroup K such that G = HK and H∩ K is s-quasi normal embedded in G.The following result is established: Let G be a group such that G is S4-free. Also let p be the smallest prime dividing the order of G and P a Sylow p-subgroup of G. If every minimal subgroup of P of order p or 4 (when p = 2) is weakly c*-normal in NG(P) and when p = 2 P is quaternion-free, then G is p-nilpotent.The main result is established and a generalization of some authors’.
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