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1.
给一个图G,定义σ3(G)=min{Σ^3i=1d(vi)│{v1,v2,v3}}是G的无关集},p3(G)=min{│U^3i=1N(vi)‖{v1,v2,v3}是G中使│n^3i=1N(vi)│≠0}的无关集}。本文证明了:设G是n阶1-坚韧图,如果σ3(G)≥n,则G包含长度至少为min{n,2p3(G)+4}的圈,为个结果推广了若干已知结果,也解决了Broersma-Heuvel-Veld 相似文献
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本文证明了下面主要结果:设G是n-可解群,π是一些素数之集,若对任意p∈∩π(G),(p,n(1-n))=1,则G的π-Hall子群的个数r=k1k2...kt,每ki≡1(modp),某P∈π,且每ki整除G的一个主因子。 相似文献
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一类不能作为自同构群的奇阶群 总被引:2,自引:0,他引:2
本文考虑如下问题:怎样的有限群可以作为另一个有限群的全自同构群?我们首先证明,若有限群K有一个正规Sylowp-子群使得|K:Z(K)|p=p2,那么K有2阶自同构.利用这个结果,我们证明了,若奇阶群G具有阶Psm(1≤s≤3),p为|G|的最小素因子,pm,m无立方因子,则G不可能作为全自同构群. 相似文献
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本文研究n阶时滞差分方程的边值问题:x(k+n)=f(k,xk(),x(k),x(k+1),…,x(k+n-1)),k∈IT,x(m)=φ(m),m∈I-r,x(1)=a1,x(2)=a2,…,x(n-2)=an-2,x(T)=A,{得到了解的存在性和唯一性的结果. 相似文献
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祁永成 《数学年刊A辑(中文版)》1994,(3)
投{Xn,n≥1}i.i.d.,Xn,1≤Xn,2≤…≤Xn,n是X1,X2,…,Xn的次序统计量.对非负整数k,r,k+r≤n,令.本文研究当k=kn,r=rn满足min(k,r)→∞,max(k,r)→0时截断和Sn(k,r)的弱大数律.设βn>0,Cn∈R,文中给出了依概率收敛的充要条件. 相似文献
7.
本文研究了一类具有中间亏指数的正系数的对称微分算式=0(-1)kDkeanxDk及=0(-1)kakDkeanxDk,证明了它们的亏指数的值域是(n,n+2,…,2n-1)或{n,n+ 2,…,2n-2 },或是一个子集合,并给出了具中间亏指数的算式的例子·这些例子表明具正系数的对称微分算式不一定都是极限点的,从而对 Everitt W. N.[1]提出的猜测又以一种新的方式给出了否定的回答.本文还得到了一类非对称的微分算式一些相应的结果. 相似文献
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设d,a,k,n是适合4k2n+1=da2,k>1,n>2,d无平方因子的正整数;又设C(K)和h(K)分别是实二次域K的理想类群和类数.本文证明了:当a<0.5k0.56n时,则h(k)=0(modn)和C(K)必有n阶循环子群. 相似文献
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形如 的正项级数,如果对m阶导数f(m)(x),存在一个幂函数xp+m(p>0),使得limXp+mf(x)(x)=k(0≤k<+ ).则当P>1,k<+ 时.级数收敛;当p≤1.k>0时。级数发散. 相似文献
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In this paper, we prove that if a torsion nilpotent group G is a weak semi-radicable group, then every Sylow p-group Gp is a central-by-finite p-group, and moreover Gp's center ζ(GP) satisfies |ζ(GP) : (ζ(GP))P| <∞, that is, ζ(GP) = D×F, where D is a divisible Abelian group, and F is a finite Abelian group. 相似文献
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A. N. Starkov 《Mathematical Notes》1998,63(2):233-241
A criterion for a wide class of topological groups which includes linear discrete groups and Lie groups to be Tychonoff groups
is established. The main result provides a criterion for an almost polycyclic group to have the Tychonoff property. By the
well-known Tits alternative, this yields the required criterion for linear discrete groups. In conclusion it is pointed out
that a particular case of the presented proof yields a Tychonoff property criterion for Lie groups. In addition, an example
of a polycyclic group without Tychonoff subgroups of finite index is constructed.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 269–279, February, 1998.
The author wishes to express his gratitude to R. I. Grigorchuk for setting the problem and his interest in the work.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00182 and by the American Mathematical
Society Fund. 相似文献
13.
N. G. Khisamiev 《Siberian Mathematical Journal》2009,50(1):181-187
We consider a torsion-free nilpotent R p -group, the p-rank of whose quotient by the commutant is equal to 1 and either the rank of the center by the commutant is infinite or the rank of the group by the commutant is finite. We prove that the group is constructivizable if and only if it is isomorphic to the central extension of some divisible torsion-free constructive abelian group by some torsion-free constructive abelian R p -group with a computably enumerable basis and a computable system of commutators. We obtain similar criteria for groups of that type as well as divisible groups to be positively defined. We also obtain sufficient conditions for the constructivizability of positively defined groups. 相似文献
14.
Spectra of finite linear and unitary groups 总被引:1,自引:0,他引:1
A. A. Buturlakin 《Algebra and Logic》2008,47(2):91-99
The spectrum of a finite group is the set of its element orders. An arithmetic criterion determining whether a given natural
number belongs to a spectrum of a given group is furnished for all finite special, projective general, and projective special
linear and unitary groups.
Supported by RFBR (grant Nos. 08-01-00322 and 06-01-39001) and by the Council for Grants (under RF President) and State Aid
of Leading Scientific Schools (project NSh-344.2008.1).
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Translated from Algebra i Logika, Vol. 47, No. 2, pp. 157–173, March–April, 2008. 相似文献
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Dikran N. Dikranjan 《代数通讯》2013,41(15):6073-6090
We study classes of abelian groups related to sequential com¬pactness and its generalizations (completeness, coarseness and sequential pre-compactness) in convergence groups. In particular, we describe the algebraic structure of the abelian groups on which every coarse convergence is complete and we prove that: i) every abelian group admits a sequentially precompact convergence; ii) every algebraically compact abelian group admits a sequen¬tially compact convergence. 相似文献
16.
Let {ie166-01} be a set of finite groups. A group G is said to be saturated by the groups in {ie166-02} if every finite subgroup
of G is contained in a subgroup isomorphic to a member of {ie166-03}. It is proved that a periodic group G saturated by groups
in a set {U3(2m) | m = 1, 2, …} is isomorphic to U3(Q) for some locally finite field Q of characteristic 2; in particular, G is locally finite.
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Translated from Algebra i Logika, Vol. 47, No. 3, pp. 288–306, May–June, 2008. 相似文献
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In this paper, we completely determine the structure of the unit group of the group algebra of some dihedral groups D2 n over the finite field Fpk, where p is a prime. 相似文献
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51. IntroductionIt is quite clear that the ekistence of complements for some families of subgroups of agroup gives a lot ofinfor~ion about its structure. FOr instance, Hall[6] proved that a groupG is supersoluble with elementary abelian Sylow subgroups if and only if G is complemellted,that is, every subgroup of G is comPlemeded in G. The same anchor also proved that agroup is soluble if and only if every Sylow subgroup is complemellted (see [3;I,3.5]). Morerecelltly, Arad and Wardll] pro… 相似文献
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