Study of S-quasi normally Embedded Subgroups and Nearly SS-embedded Subgroups in the Symmetry Group S4
In order to investigate all S-quasinormal subgroups,S-quasinormally embedded subgroups and near-ly SS-embedded subgroups of the quartic symmetry group S4,the corresponding results are obtained by using the definition and correlation lemma,combined with the calculation method of permutation.The results show that the S-quasinormal subgroups of S4 are N1,K4,A4,S4;the S-quasinormally embedded subgroups of S4 are N1,Ni1,N12,N13,N14,K4,N26,N27,N28,A4,S4;the nearly SS-embedded subgroups of S4 are N1,N2,N3,N4,N5,N6,N7,N11,N12,N13,N14,K4,N22,N23,N24,N25,N26,N27,N28,A4,S4.
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