On S-quasinormal and c-normal subgroups of a finite group |
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Authors: | Shirong Li Yangming Li |
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Affiliation: | (1) Department of Mathematics, Guangxi University, Nanning, Guangxi, 530 004, China;(2) Department of Mathematics, Guangdong College of Education, Guangzhou, 510 310, China |
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Abstract: | Let be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are presented: (1) G ∈ if and only if there is a normal subgroup H such that G/H ∈ and every maximal subgroup of all Sylow subgroups of H is either c-normal or S-quasinormally embedded in G. (2) G ∈ if and only if there is a normal subgroup H such that G/H ∈ and every maximal subgroup of all Sylow subgroups of F*(H), the generalized Fitting subgroup of H, is either c-normal or S-quasinormally embedded in G. (3) G ∈ if and only if there is a normal subgroup H such that G/H ∈ and every cyclic subgroup of F*(H) of prime order or order 4 is either c-normal or S-quasinormally embedded in G. Supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangxi Autonomous Region (No. 0249001). Corresponding author. Supported in part by the Natural Science Foundation of China (10571181), NSF of Guangdong Province (06023728) and ARF(GDEI). |
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Keywords: | S-quasinormally embedded subgroup c-normal subgroup p-nilpotent group the generalized Fitting subgroup saturated formation |
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