SOME RESULTS ON P-GROUPS

In this paper , we define a certain subgroup ,denoted by Z *(G) ,as follows : Z * (G) {x Z (G) : x p  e} of a finite group G , and we give some properties of Z *(G) . Main result for Z *(G) is given in theorem 3.5 , which state that G is an elementary abelian p  group if and only ifG  Z *(G).