en عمومى General پژوهشي Research paper <p style="text-align: justify;">Let &sigma; = {&sigma;_i|i &isin; I} be a partition of the set of all primes P and G a finite group. A set H of subgroups of G is said to be a complete Hall &sigma;-set of G if every member&ne; 1 of H is a Hall &sigma;_i-subgroup of G for some i &isin; I and H contains exactly one Hall &sigma;_i-subgroup of G for every i such that &sigma;_i &cap;&pi;(G)&ne; &empty;. In this paper, we study the structure of G based on the notion of &sigma;-conditionally permutable subgroups.</p> Finite groups, σ-conditionally permutable subgroups, Supersoluble groups, σ-nilpotent subgroups, Complete Hall σ-set. 13 19 http://ijmsi.ir/browse.php?a_code=A-10-6802-1&slc_lang=en&sid=1 Muhammad Tanveer Hussain tanveerhussain@umt.edu.pk 100319475328460012018 100319475328460012018 Yes Department of Mathematics, University of Management and Technology Lahore 54770, Pakistan