Let G be a group. Neumann to answer a question of Paul Erdos proved that every infinite subset of G has two different comuting elements  if and only if G is center-by-finite. In this paper, we deal with Erdoschr('39')s question in different aspect and we show that every infinite subset X of G has two different elements x and y such that x^y=1  if and only if the exterior  center of G ihas finite index.

Keywords: Problem of Paul Erdös, Infinite groups, 〖FC〗^˄- group, Central- by- finite, Exterior abelian, Exterior center of group.

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