The Weakly-complementded Subgroups Of Finite Groups

The properties of subgroups are used by many scholars to charcterise thestructure of finitc groups. Minimal subgroups, i.e.subgroups with prime order, takea special important part in investigating the p-nilpotency. A well-known resultdue to Ito states that a group G is p-nilpotent if every element of order p liesin the center of G, and if p=2 elements of G with order 4 are also in thecenter of G. In this paper, we mainly use weakly complemented subgroups tocharacterise the structure of finite groups and obtain some results like Ito's theo-rem in the chapterⅠ. In the next chapter we investigate the relation between theweakly-complemented subgroups of P∩G' and p-nilpotency, and generalize theBurnside's theorem. In the last chapter, according to the theory of formations, we obtain some sufficient conditions of saturated formation, and generalize someknown theorems.