University of TehranJournal of Sciences, Islamic Republic of Iran1016-110424420131201Some properties of n-capable and n-perfect groups36136436457ENM. R.RismanchianDepartment of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Islamic Republic of Iran.Journal Article20130707In 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