**Author(s): ** Shitian Liu**Journal: ** Asian Journal of Algebra ISSN 1994-540X

**Volume: ** 2;

**Issue: ** 1;

**Start page: ** 17;

**Date: ** 2009;

VIEW PDF DOWNLOAD PDF Original page**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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