Abstract
The normalizer of each Sylow subgroup of a finite group G has a nilpotent Hall supplement in G if and only if G is soluble and every tri-primary Hall subgroup H (if exists) of G satisfies either of the following two statements: (i) H has a nilpotent bi-primary Hall subgroup; (ii) Let π(H) = {p, q, r}. Then there exist Sylow p-, q-, r-subgroups H p , H q , and H r of H such that H q ⊆ N H (H p ), H r ⊆ N H (H q ), and H p ⊆ N H (H r ).
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Original Russian Text Copyright © 2009 Li B., Guo W., and Huang J.
The authors were supported by the NNSF of P. R. China (Grant 10771180), the Scientific Research Fund of the Sichuan Provincial Education Department (Grant 08zb059), and the Research Program of the Chengdu University of Information Technology (Grant KYTZ200909).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 4, pp. 841–850, July–August, 2009.
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Li, B., Guo, W. & Huang, J. Finite groups in which Sylow normalizers have nilpotent Hall supplements. Sib Math J 50, 667–673 (2009). https://doi.org/10.1007/s11202-009-0075-7
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DOI: https://doi.org/10.1007/s11202-009-0075-7