Let σ = {σi|i ∈ 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 σ-set of G if every member≠ 1 of H is a Hall σi-subgroup of G for some i ∈ I and H contains exactly one Hall σi-subgroup of G for every i such that σi ∩π(G)≠ ∅. In this paper, we study the structure of G based on the notion of σ-conditionally permutable subgroups.
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