| 苏宁,李样明,王燕鸣.关于有限群子群的弱s-可补性[J].数学年刊A辑,2015,36(1):91~102 |
| 关于有限群子群的弱s-可补性 |
| The Weakly s-Supplemented Property of Finite Groups |
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| DOI： |
| 中文关键词: 弱s-可补子群,
p-幂零群, ${\cal U}$-超中心, p-可解群的p-长 |
| 英文关键词:Weakly s-supplemented subgroup,
p-Nilpotent group, ${\cal U}$-Hypercenter,p-Length of a
p-solvable group |
| 基金项目:国家自然科学基金 (No.11401597, No.11171353, No.11271085), 广东省自然科学基金 (No.S2011010004447) 和广东省高校学科建设专项项目(No.2012KJCX0081) |
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| 中文摘要: |
| H是G的一个子群. 称H为G的一个s-置换子群,
若对于G的任意Sylow 子群P, 成立HP = PH.
称H为G的一个弱s-可补的子群.
若存在G的一个子群T, 使得G=HT且H\cap T \leq H_{{\rm s}G},
其中H_{{\rm s}G}是包含在H中的G的最大的s-置换子群.
本文在假设G的某些子群是弱s-可补的前提下,
得到了G的一个结构定理, 并推广了许多近期的结果. |
| 英文摘要: |
| Suppose that G is a finite group and H is a subgroup of G. H is
said to be s-permutable in G if HP = PH for any Sylow
subgroup P of G. H is said to be weakly s-supplemented in
G if there is a subgroup T of G, such that
G=HT and H\cap T \leq H_{{\rm s}G}, where H_{{\rm s}G} is the biggest
s-permutable subgroup of G contained in H. In this paper, a
structural theorem of finite groups is given under the
hypothesis that some subgroups of G are weakly s-supplemented
subgroups of G. Many recent results are extended. |
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