Finite groups in which Sylow normalizers have nilpotent Hall supplements |
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| Authors: | Baojun Li Wenbin Guo Jianhong Huang |
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| Institution: | (1) Chengdu University of Information Technology, Chengdu, P. R. China;(2) Xuzhou Normal University, Xuzhou, P. R. China;(3) University of Science and Technology of P. R. China, Hefei, P. R. China |
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| 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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| Keywords: | finite group Sylow subgroup normalizer nilpotent Hall supplement soluble group |
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