Permutability of minimal subgroups andp-nilpotency of finite groups
In this paper it is proved that ifp is a prime dividing the order of a groupG with (|G|,p − 1) = 1 andP a Sylowp-subgroup ofG, thenG isp-nilpotent if every subgroup ofP ∩G N of orderp is permutable inN G (P) and whenp = 2 either every cyclic subgroup ofP ∩G N of order 4 is permutable inN G (P) orP is quaternion-free. Some applications of this result are given.
KeywordsNormal Subgroup Finite Group Maximal Subgroup Prime Order Cyclic Subgroup
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- [R]D. J. S. Robinson,A Course in the Theory of Groups, Springer-Verlag, New York-Berlin, 1993.Google Scholar