Abstract
Let σ = {σ i | i ∈ I} be a partition of the set of all primes P, and let G be 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 σ i -subgroup of G for some i ∈ I and H contains exactly one Hall σ i -subgroup of G for every i such that σ i ∩ π(G) ≠ ∅. In this paper, we study the structure of G under the assuming that some subgroups of G permutes with all members of H.
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Acknowledgements
The authors are very grateful for the helpful suggestions of the referees. This work was supported by the National Natural Science Foundation of China (Grant No. 11301227) and the Natural Science Foundation of Jiangsu Province (No. BK20130119).
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Yin, X., Yang, N. Finite groups with permutable Hall subgroups. Front. Math. China 12, 1265–1275 (2017). https://doi.org/10.1007/s11464-017-0641-4
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DOI: https://doi.org/10.1007/s11464-017-0641-4