关于ss-拟正规子群和c-正规子群 |
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引用本文: | 程丹,徐颖吾.关于ss-拟正规子群和c-正规子群[J].云南民族大学学报(自然科学版),2019(3):251-253. |
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作者姓名: | 程丹 徐颖吾 |
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作者单位: | 西安工程大学理学院 |
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摘 要: | 设G是有限群,H是G的子群.称H在G中ss-拟正规,如果H存在1个补子群B,满足H和B的每个Sylow子群可以交换.称H在G中c-正规,如果存在G的正规子群K,使得G=HK且H∩K≤H_G,这里H_G是H在G中的正规核.同时考虑这2个概念,并应用群论研究的"或"思想方法,得出的主要结论是:当p是满足|G|的素因子且■是G的1个Sylow p-子群,如果P的极大子群在G中c-正规,或在G中ss-拟正规时,群G是p-幂零群.
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关 键 词: | 有限群 Sylow子群 极大子群 ss-拟正规子群 c-正规子群 p-幂零 |
On ss-quassinormal subgroups and c-normal subgroups |
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Abstract: | Let G be a finite group, H is a subgroup of G. A subgroup H is said to be an ss-quassinormal subgroup of G, if there is a supplement B of H to G such that H permutes with every Sylow subgroup of B. However, A subgroup H of G is called c-normal in G provided that there exists a normal subgroup K such as G=HK and H∩K≤H_G, where H_G is the normal core of H in G. The two concepts are considered in a group at the same time, and we apply the "or" method of group theory to the research. It concludes as follows: suppose p a prime dividing |G| with(|G|,p-1)=1 and let P be a Sylow p-subgroup of a group G, and if every maximal subgroup of P is either ss-quassinormal or c-normal, then G is p-nilpotent. |
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Keywords: | finite group subgroup maximal subgroup ss-quasinormal subgroup c-quasinormal subgroup p-nilpotent |
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