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超可解群的若干充分条件 总被引:12,自引:1,他引:11
关于有限超可解的研究已有不少结果,本文在苏向盈研究有限群的半正规子群的基础上又得到了一系列新的结果(文中定理2—9),本文还对[1]中定理6的证明进行了改进并得到了重要推论,改进的方法在本文得到了充分应用.文中所说群均为有限群,使用的符号是规范的. 相似文献
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关于p-超可解群的若干充分条件王品超,李文祥(山东曲阜师范大学数学系,273165)(山东滨州师专数学系,256604)关键词P-超可解群,p-sylow子群.分类号AMS(1991)20D20/CCLO152本文定理1推广了[1](p88)中定理8... 相似文献
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In this paper, we give some sufficient conditions for products of two supersolvable sub-groups to be supersolvable groups. Our results generalize some known results.Theorem 1 Let G = HK,(|H|,|K|) = 1, Where H and K are two supersolvable sub-groups. If H is commutative with every maximal subgroup of K, and K is commutative with every maximal subgroup of H, then G is supersolvable.Theorem 2 Let G = HK, H ∩ K = 1, H G, and K be quasinormal in H. If H, K are supersolvable, the G is supersolvable.Theorem 3 Let G= HK,(|H|,|K|) = 1,H,K be two supersolvable subgroups. If H is commutative with any Sylow subgroup of K and any maximal subgroup of every sylow subgroup of K, and K is commutative with any sylow subgroup of H and any maximal subgroup of every sylow subgroup of H, then G is supersolvable. Theorem 4 If H,K are two supersolvable subgroups of G, G= HK, G′is nilpotent, H is quasi normal K, and K is quasi normal in H,then G is supersolvable. Theorem 5 If H,K are two supersolvable subgroups of G, G= HK, H′? G,[H,K]? G,[H,K] is nilpotent, H is quasi normal in K, and K is quasi normal in H,then G is supersolvable. 相似文献
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s-半置换子群对有限群的p-超可解性的影响 总被引:1,自引:0,他引:1
群G的子群H称为半置换的,若对任意的K≤G,只要(|H|,|K|)=1,就有HK=KH.H称为s-半置换的,若对任意的p||G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文研究Sylow子群的极大子群及极小子群的s-半置换性对有限群的p-超可解性的影响. 相似文献
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A subgroup if of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|, |K|) - 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. In this paper, some sufficient conditions for a group to be solvable are obtained in terms of s-semipermutability. 相似文献
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n-极大子群为共轭可换的有限群 总被引:2,自引:0,他引:2
赵俊英 《纯粹数学与应用数学》2004,20(2):177-181
群G的子群H称为G的共轭可换子群,若HHg=HgH,对任意g∈G都成立,本文考查了n-极大子群为共轭可换时对有限群构造的影响. 相似文献
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ON F-z-SUPPLEMENTED SUBGROUPS OF FINITE GROUPS 总被引:1,自引:0,他引:1
A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F(G), where Z∞F(G) is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups. 相似文献
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Let G be a finite group and OutCol(G) the Coleman outer automorphism group of G(for the definition, see below). The question whether OutCol(G) is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime.In this article, some sufficient conditions for OutCol(G) to be a p′-group are obtained. Our results generalize some well-known theorems. 相似文献
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若有限群G的每个2-极大子群在G中次正规,则称G为SMSN-群.本文研究了有限群G的每个真子群是SMSN-群但G本身不是SMSN-群的结构,利用局部分析的方法,获得了这类群的完整分类,推广了有限群结构理论的一些成果. 相似文献
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有限群G的子群H称为G的BNA子群,若对任意的x∈G有H^(x)=H或x∈.若有限群G的所有素数阶和4阶循环子群都是G的BNA子群,则称G为CBNA群.本文主要刻画CBNA群的结构,并且给出所有真子群都是CBNA群的完全分类. 相似文献
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本文研究了有限群的超可解性.利用Fitting子群的某些特殊子群的PCM性质对有限群结构的影响,获得了超可解群的一些充要条件. 相似文献
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本文研究了有限群G的Coleman外自同构群是p'-群这个问题. 利用Sylow p-子群和同调群的性质,得到了有限群的Coleman外自同构群是p'-群的一些充分条件,其结果与M.Hertweck和W.Kimmerle得到的结果是不同的. 相似文献
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1IntroductionThenotationandtelliluologyusedwillmainlyconformtothatof[5].Werecall11ereafewfundamentalnotions.Inthispaper,groupmeansabeliangroup,qdenotestheadditivegroupOfrationals,ZdenotesthegroupOfintegers.Atypeisanequivalenceclassofheightsequences.IfSisafinitesetoftypestheniuf(S)andsup(S)aretypes,whereinf(S)andsup(S)aregivenbycomponentndninlumsandmaximumsofheightsequencesrepresentingtypesinS.Twotorsionfi'eegroupsAandBarequasi-isolllorphicifthereisfEHorn(A,B)suchthatIisamonomorphismand… 相似文献
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群G的子群H称为G的CAP-嵌入子群,如果对于|H|的每个素因子p,存在G的某个CAP-子群K,使得H的某个Sylow p-子群也是K的一个Sylowp-子群.本文通过假定G的p-Fitting子群F_p(G)的某个Sylow p-子群的每个极大子群是G的CAP-嵌入子群,得到一些新的结果. 相似文献