University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 24 4 2013 12 01 Some properties of n-capable and n-perfect groups 361 364 36457 EN M. R. Rismanchian Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Islamic Republic of Iran. Journal Article 2013 07 07 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. https://jsciences.ut.ac.ir/article_36457_52c4a08f484812fbb2c22163f5342e7b.pdf