cs-Normal Subgroups of Finite Groups

The relationship between the subgroups of a finite group G and the structure of G has been extensively studied in group theory. It is interesting to use some information on the subgroups of a finite group G to determine the structure of a group G, so from the beginning's of group theory we see that some scientists interest in this side. The normality of subgroups of a finite group plays an important role in the studying of a finite group. Recently, the concepts of cs-normal subgroups was introduced by AL-Tahat in his M. Sc. thesis as a generalization for weakly c-normal subgroups by replaced the normal condition with the subnormal condition in the definition of weakly c-normal subgroup, and used the cs- normality to determine the structure of some groups. As well as, several examples and properties of cs- normal subgroups were proved. Throughout this thesis, all groups considered are finite. The main goal of this thesis is to study some properties of weakly c-normal and cs- normal subgroups of a finite group, and to use the weakly c-normality and cs-normality of some Sylow and maximal subgroups to determine the Structure of some finite groups.

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Holds a bachelor's and master's degree in mathematics. He joined the Mathematics Department at AL-Balqa' Applied University, where he taught full time. He devoted the majority of his time to taught, writing papers, textbook and activities for mathematics.He has published numerous papers in Algebra, Differential Geometry and applied Mathematics.