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X-可换子群与有限群的超可解性
引用本文:刘玉凤.X-可换子群与有限群的超可解性[J].四川轻化工学院学报,2008(4):1-2.
作者姓名:刘玉凤
作者单位:[1]山东工商学院数学与信息科学学院,山东烟台264005
基金项目:基金项目:国家自然科学基金资助项目(10771180)
摘    要:利用X-可换子群的概念,得到了有限群超可解的2个充分条件:(1)设G是可解群,石是G的子集且包含G的极小子群和极大子群。如果G的每个极大子群和G的sylow子群的每个极大子群在G中X-可换,那么G是超可解群;(2)设足签,X是G的子集且包含G的p-子群。如果每个不包含K的G的极大子群在G中X-可换,那么K是超可解群。

关 键 词:有限群  X-可换子群  极大子群  超可解群

X-permutable Subgroups and Supersolubility of Finite Groups
LIU Yu-feng.X-permutable Subgroups and Supersolubility of Finite Groups[J].Journal of Sichuan Institute of Light Industry and Chemical Technology,2008(4):1-2.
Authors:LIU Yu-feng
Affiliation:LIU Yu-feng (School of Mathematics and Informational Science, Shandong Institute of Business and Technology, Yantai 264005, China )
Abstract:Using the concept, X-permutable subgroup of finite groups, two sufficient conditions of supersoluble groups are obtained:(1) G is a soluble group, let X be a subgroup of G such that X contains every maximal subgroup and every minimal subgroup of G.Suppose that every maximal subgroup of G is X-permutable with every maximal subgroup of every Sylow subgroup of G in G, then G is a supersoluble group;(2)Let K be a normal subgroup of G, let X be a subgroup of G such that X contains every p-subgroup of G. Suppose that every maximal subgroup of G not containing K is X-permutable in G, then K is a supersoluble group.
Keywords:finite group  X-permutable subgroup  maximal subgroup  supersoluble group
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