| 有限群的ss-置换子群 |
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| 引用本文： | 卢家宽,郭秀云.有限群的ss-置换子群[J].纯粹数学与应用数学,2010,26(4):587-596. |
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| 作者姓名： | 卢家宽 郭秀云 |
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| 作者单位： | 广西师范大学数学科学学院,广西,桂林,541004;上海大学数学系,上海,200444 |
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| 基金项目： | 国家自然科学基金，SGRC，上海市教委重点学科建设项目 |
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| 摘 要： | 设G为有限群,称G的子群H为ss-置换子群,如果存在G的次正规子群B使得G=HB,且H与B的任意Sylow子群可以交换,即对任意X∈Syl（B）有XH=HX.利用子群的ss-置换性来研究有限群的结构,得到有限群超可解的两个充分条件.
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| 关 键 词： | ss-置换子群 s-置换子群 超可解群 |
On ss-permutable subgroups of finite groups |
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| LU Jia-kuan,GUO Xiu-yun.On ss-permutable subgroups of finite groups[J].Pure and Applied Mathematics,2010,26(4):587-596. |
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| Authors: | LU Jia-kuan GUO Xiu-yun |
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| Institution: | LU Jia-kuan 1,GUO Xiu-yun 2(1.Department of Mathematics,Guangxi Normal University,Guilin 541004,China,2.Department of Mathematics,Shanghai University,Shanghai 200444,China) |
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| Abstract: | A subgroup H of a finite group G is called to be ss-permutable in G if G has a subnormal subgroup B such that HB = G and HS = SH for any Sylow subgroup S of B.We fix in every non-cyclic Sylow subgroup P of G a subgroup D satisfying 1 < |D| < |P| and study the structure of G under the assumption that all subgroups H with |H| = |D| are ss-permutable in G. |
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| Keywords: | ss-permutable subgroups s-permutable subgroups supersolvable groups |
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