In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.

mokr?n, an iranian district, is located south of baluchistan on northern coasts of mokr?n (oman) sea. its particular geographical situation has caused a promoting economic position since longs ago and its harbors have had an excellent commercial position and a significant economic improvement through the history. mokr?n benefits a thousands-year history and precious civilization. there are diff...