Document Type : Original Paper

Author

• M. R. Rismanchian

Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Islamic Republic of Iran.

Abstract

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.

Keywords

• n-central
• n-capable
• n-perfect
• n-unicentral