Classification of finite simple groups and p-groups with a special property on their conjugacy classes

Let G be a finite group and let G x denotes the conjugacy class of anelement x of G . We say that group G satisfies property Ui , i ۱, ifunion of any i distinct non-trivial conjugacy classes of G together with۱ is a subgroup of it. In this paper, we classify all finite simple groups Gthat satisfy property ۵ U and we prove that there is no finite p - groupsatisfying property ۵ U .

Keywords:

Conjugacy class , Simple group , Rational group