共查询到20条相似文献,搜索用时 62 毫秒
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群G的子群H称为G的弱s-拟正规子群,若G有次正规子群T,使得G=HT且H ∩T≤HsG,其中HsG是包含在H中的G的最大的s-拟正规子群.本文利用Sylow p-子群的极大子群的弱s-拟正规性得到有限群为p-幂零群的一些充分条件,并给出Schur-Zassenhaus定理的一种推广. 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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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).本文利用Sylow子群的2-极大子群的s-半置换性得到有限群为p-幂零群的一些充分条件. 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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《数学的实践与认识》2013,(20)
有限群G的子群H称为G的s-半置换子群,若H与G的每个满足条件(p,|H|)=1的Sylow p-子群可置换.若有限群G的每个极小子群和4阶循环子群都在G中s-半置换,则称G为MSS-群.给出群G的每个真子群是MSS-群但G本身不是MSS-群的分类. 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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只具有半正规和反正规子群的有限群 总被引:1,自引:0,他引:1
群G的子群H称为是G的半正规子群,若对任意G的子群K,只要K的阶数与H互质,则H与K可置换;称H在G中是反正规的,若对任意g∈G,g,∈<H.Hg>.本文刻画了每个子群是半正规的,或反正规的有限群,推广了[1]及[2]中的结果. 相似文献
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有限群的s-条件置换子群 总被引:15,自引:0,他引:15
如果对群G的任意Sylow子群T,存在一个元素x∈G,使得HTx=TxH,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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Following Rose, a subgroup H of a group G is called contranormal, if G = H G . In certain sense, contranormal subgroups are antipodes to subnormal subgroups. It is well known that a finite group is nilpotent if and only if it has no proper contranormal subgroups. However, for the infinite groups this criterion is not valid. There are examples of non-nilpotent infinite groups whose subgroups are subnormal; in paricular, these groups have no contranormal subgroups. Nevertheless, for some classes of infinite groups, the absence of contranormal subgroups implies the nilpotency of the group. The current article is devoted to the search of such classes. Some new criteria of nilpotency in certain classes of infinite groups have been established. 相似文献
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关于有限群的$CAP$-嵌入子群 总被引:1,自引:0,他引:1
A subgroup H of a finite group G is said to be CAP-embedded subgroup of G if, for each prime p dividing the order of H, there exists a CAP-subgroup K of G such that a Sylow p-subgroup of H is also a Sylow p-subgroup of K. In this paper some new results are obtained based on the assumption that some subgroups of prime power order have the CAP-embedded property in the group. 相似文献
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A subgroup of a group G is said to be Sylow-quasinormal (S-quasinormal) in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be Supplement-Sylow-quasinormal (SS-quasinormal) in G if there is a supplement B of H to G such that H is permutable with every Sylow subgroup of B. In this article, we investigate the influence of SS-quasinormal of maximal or minimal subgroups of Sylow subgroups of the generalized Fitting subgroup of a finite group. 相似文献
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本文以根系及Weyl群为基础,以换位子公式为工具,对任意域上任意类型Chevalley群,针对极大抛物子群情形,确定了Levi子群在抛物子群中的所有扩群. 相似文献
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Guo和Chen在2010年引入了弱c-可置换子群的概念,并利用这种新的广义置换性质对有限群的结构给出了一些新的刻画.本文推广了上述文献中的两个主要结论,确定了极小子群为弱c-可置换子群的有限群的结构. 相似文献
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假定Fitting子群F(G)或广义Fitting子群F*(G)的某些子群在G中SQ-补来研究包含超可解群的饱和群系s,这里G∈s.一些已知结果被推广. 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) ∈ N~3 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 describes the characteristic subgroups of a given metacyclic p-group when p ≥ 3. A "reciprocity" relation on enumeration of subgroups of a metacyclic group is also given. 相似文献
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For a finite group G, let v(G) denote the number of conjugacy classes of non-normal subgroups of G and vc(G) denote the number of conjugacy classes of non-normal noncyclic subgroups of G. In this paper, we show that every finite group G satisfying v(G) ≤2|π(G)| or vc(G) ≤ |π(G)| is solvable, and for a finite nonsolvable group G, v(G) = 2|π(G)| +1 if and only if G ? A 5. 相似文献
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关于有限群的S-半置换子群 总被引:1,自引:0,他引:1
Let d be the smallest generator number of a finite p-group P and let Md(P) = {P1,...,Pd} be a set of maximal subgroups of P such that ∩di=1 Pi = Φ(P). In this paper, we study the structure of a finite group G under the assumption that every member in Md(Gp) is S-semipermutable in G for each prime divisor p of |G| and a Sylow p-subgroup Gp of G. 相似文献