共查询到18条相似文献,搜索用时 46 毫秒
1.
如果对群G的任意Sylow子群T,存在一个元素x∈G,使得HT~x=T~xH,那么称群G的子群H在G中s-条件置换.利用s-条件置换子群给出了一些群的性质和结构. 相似文献
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设H为G的子群,称H在G中半置换,如果HK=KH对任意满足条件(|H|,|K|)=1的G的子群K都成立;称H在G中s-半置换,如果HP=PH对任意P∈Sylp(G)都成立,其中(|H|,p)=1.这两个概念自陈重穆1987年提出后,获得国内外许多学者的关注,应用此概念近几十年来有大量的文章出现.本文对这方面的成果进行总结,给出研究过程中的思路. 相似文献
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设G为有限群,G的一个子群H称为半置换的,若对任意的K≤G,只要(|K|,|H|)=1,就有KH=HK;H称为s-半置换的,若对任意的p||C|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文考察了素数幂阶子群的s-半置换性对有限群的超可解性的影响. 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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Let X be a nonempty subset of a group G.A subgroup H of G is said to be X-s-permutable in G if there exists an element x ∈ X such that HPx = PxH for every Sylow subgroup P of G.In this paper,some new results are given under the assumption that some suited subgroups of G are X-s-permutable in G. 相似文献
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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. 相似文献
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称有限群G的子群H在G中s-半置换,如果H与G的每个Sylowp-子群可换,其中(p,|H|)=1.本文研究了s-半置换子群对有限群结构的影响.. 相似文献
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s-半置换子群对群构造的影响 总被引:17,自引:0,他引:17
群G的一个子群H称为半置换的,若对G的任意子群K,只要(|H|,|K|)=1,就有HK=KH;H称为s-半置换的,若对G的任意Sylow p-子群P,只要(p,|H|)=1,就有HP=PH.本文研究极大子群和极小子群的某些子群的s-半置换性对群构造的影响,推广和改进了Asaad及王品超等人所得的结果. 相似文献
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有限群极大子群的θ-子群偶 总被引:21,自引:0,他引:21
N.P.Mukherjee和 P.Bhattacharya在“On theta pairs for a maximal sub-group”(Proc.Amer.Math.Soc,Vl09N3(1990))一文中定义了有限群的极大子群的θ-子群偶概念,研究了极大子群的极大θ-子群偶对群结构的影响,得到了一系列结果.本文在进一步探究θ-子群偶性质的基础上,对该文中一系列主要结果作出了本质性的改进,并给出了可解性、幂零性的一些新刻划. 相似文献
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殷霞 《数学的实践与认识》2012,42(5):164-169
研究了有限群的结构问题,利用子群c-半置换和完全c-半置换的定义和性质,通过对有限群sylow子群的2-极大子群的研究,获得了有限群幂零、p-幂零的充分条件和另外两个决定群结构的充要条件. 相似文献
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Manuel J. Alejandre A. Ballester-Bolinches M. C. Pedraza-Aguilera 《Journal of Algebra》2001,240(2):207
A finite group G is said to be a PST-group if every subnormal subgroup of G permutes with every Sylow subgroup of G. We shall discuss the normal structure of soluble PST-groups, mainly defining a local version of this concept. A deep study of the local structure turns out to be crucial for obtaining information about the global property. Moreover, a new approach to soluble PT-groups, i.e., soluble groups in which permutability is a transitive relation, follows naturally from our vision of PST-groups. Our techniques and results provide a unified point of view for T-groups, PT-groups, and PST-groups in the soluble universe, showing that the difference between these classes is quite simply their Sylow structure. 相似文献
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It is proved that if G = AB is a soluble group with finite abelian section rank which is factorized by two mutually permutable finite-by-nilpotent subgroups A and B such that A′ and B′ are locally nilpotent, then also the normal closure ? A′, B′ ?G is locally nilpotent and the subgroups A′ and B′ are ascendant in G. 相似文献
15.
Peter V. Hegarty 《Journal of Algebra》1997,190(2):556
We present some new results about the absolute center and autocommutator subgroup of a group, concepts which were introduced in an earlier paper. 相似文献
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Let G be a finite group. We fix in every noncyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P| and study the structure of G under the assumption that all subgroups H of P with |H| = |D| are c-normal in G. 相似文献
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Xu YANG 《数学年刊B辑(英文版)》2020,41(2):241-266
In this paper, the author characterizes the subgroups of a finite metacyclic group K by building a one to one correspondence between certain 3-tuples(k, l, β) ∈ N3 and all the subgroups of K. The results are applied to compute some subgroups of K as well as to study the structure and the number of p-subgroups of K, where p is a fixed prime number. In addition, the author gets a factorization of K, and then studies the metacyclic p-groups, gives a different classification, and describe... 相似文献
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Ukrainian Mathematical Journal - Let ? be a Fitting set of a group G, let π be a nonempty set of primes, and let L ≤ G. In this case, ? is called a Fischer π-set of G if... 相似文献