Abstract
Throughout this note, groups are all finite. N. It has established the following theorem concerning nilpotent groups It Theorem. Suppose that G is a group of odd order. (ⅰ) If the subgroups of prime order of G all are contained in the center of G, then G is nilpotent. (ⅱ) If the subgroups of prime order of G’all are normal in G, then G is solvable.
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