李Poisson超代数的泛中心扩张

研究了李Poisson超代数的泛中心扩张问题.通过构造其泛中心扩张,得到了其存在泛覆盖的充要条件是李Poisson超代数是完全的,并对李Poisson超代数的自同构群及导子的提升给出了结果.     

A类算子n次根的代数扩张是次标量算子

研究了A类算子n次根的代数扩张.特别地,利用空间分解技巧得到每个A类算子n次根的代数扩张是次标量算子.作为应用,考虑了此类算子的Weyl型定理和超不变子空间问题.     

经典N=2李共形超代数的导子和第二上同调群

研究了经典N=2李共形超代数的导子和第二上同调群的结构,并应用第二上同调群的结果确定了该李共形超代数的泛中心扩张.     

Topological超共形代数的Leibniz中心扩张

通过计算得到了Topological N=2超共形代数丁的Leibniz二上同调群,从而确定了此代数的Leibniz中心扩张.     

具有卷积的中心自反环

本文研究了具有卷积的中心自反环的性质,定义并引入了中心-自反环,显然,中心-自反环是自反环、中心自反环和-自反环的推广.给出了这类环的一些特征,研究了相关的环扩张,包括平凡扩张,Dorroh扩张和多项式扩张.     

Winter定理和Dietz定理的推广

设G是由中心扩张1→Z_p^m→G→Z_p×…Z_p所决定的有限p-群,且|G’|≤p.确定了G的自同构群结构,推广了Winter和Dietz的工作     

格蕴涵代数中的扩张滤子

在格蕴涵代数中提出了扩张滤子的概念,讨论了扩张滤子与滤子,扩张滤子与素滤子,扩张滤子与滤子的根,扩张滤子与准素滤子,扩张滤子与最大滤子之间的关系.得到了扩张滤子的一些性质.最后,证明了在格H蕴涵代数中,扩张滤子与扩张滤子的根相等.     

分次环的有限正规扩张

本文研究了群分次环的有限正规分次扩张问题．利用经典环论方法，得到一个群分次环与其有限正规分次扩张环之间关于分次Jacobson根和分次素根的关系，同时，给出了分次情形的Cutting down定理和Lying over定理．     

区间上满的扩张Markov自映射的迭代根

考虑区间上满的扩张 Markov自映射 ,给出了区间上满的扩张 Markov自映射具有指定阶的迭代根的充分必要条件 .     

超序列紧fts,可数超紧fts和超列紧fts

文献[1]中定义了序列紧fts(每个不分明集序列有收敛的子序列)和可数紧fts(每个可数开覆盖存在有限子覆盖)。对于序列紧fts,得到“每个fts都是序列紧的”病态结果,由此可见这样定义的序列紧fts不是一般拓扑学中序列紧的良扩张。对于可数紧fts,[2]在评论F-紧性时,论证了凡T_1空间都不是F-紧空间,以上的论证也可得到凡T_1空间都不是可数紧fts的病态结果。我们还要指出,[1]定义的可数紧fts也不是一般拓扑学中可数紧的良扩张。     

On Hypercentral Groups G With |G:G n |<∞

In 1960, Baumslag, following up on work of Cernikov for the 1940s, proved that a hypercentral p-group G with G = G ^p is a divisible Abelian group. In this article, we provide an interesting generalization of this 45 year old result: If a hypercentral p-group G satisfies |G:G ^p |<∞ (of course, it contains G = G ^p ), there exists a normal divisible Abelian subgroup D such that |G:D|<∞.     

Some Results on Hypercentral Units in Integral Group Rings

Abstract

In this note we investigate the hypercentral units in integral group rings ?G,where G is not necessarily torsion. One of the main results obtained is the following (Theorem 3.5): if the set of torsion elements of G is a subgroup T of G and if Z ₂(𝒰) is not contained in C _𝒰(T),then T is either an Abelian group of exponent 4 or a Q* group. This extends our earlier result on torsion group rings.     

On weakly-central group extensions

Some properties of weakly-central extensions for which the quotient group by the kernel is hypercentral are investigated. The existence of a hypercentral coradical in any such periodic group is proved and the complementability of some of its subgroups in the group is established.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1017–1021, July–August, 1991.     

Hypercentral groups of finite subnormal rank

We introduce the notion of subnormal rank of a group and study hypercentral groups of finite subnormal rank. We construct an example of a hypercentral group that has a finite subnormal rank and infinite (special) rank.Translated from Ukrainskii Matematicheskii Zhurnal, Vol.47, No. 11, pp. 1577–1580, November, 1995.     

Hypercentral Groups with all Subgroups Subnormal III

It is shown that a hypercentral group that has all subgroupssubnormal and every non-nilpotent subgroup of bounded defectis nilpotent. As a consequence, a hypercentral group of lengthat most in which every subgroup is subnormal is nilpotent.2000 Mathematics Subject Classification 20E15, 20F14.     

The hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra

We describe the hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra over an arbitrary field. Using it, we prove that this group admits no faithful representation by matrices over a field provided that the algebra rank is at least four.     

On the normal subgroup lattice of a hypercentral p-group

We describe all hypercentral p-groups G whose lattice of normal subgroups n(G) is isomorphic to n(H) for a group H with hypercenwal derived subgroup and H not a pgroup.     

On trifactorized soluble groups of finite rank

Let the soluble-by-finite group G=AB=AC=BC be the product of two nilpotent subgroups A and B and a subgroup C. It is shown that, if G has finite abelian section rank and C is hypercentral (hypercyclic), then G is hypercentral (hypercyclic). Moreover, if G is an L ₁-group and C is nilpotent, then G is nilpotent.Dedicated to Professor Guido Zappa on the occasion of his 75th birthday     

Hyperzyklische gruppen

Definition: (a)G is called hypercyclic «iff each epimorphic imageH≠1 ofG possesses a cyclic normal subgroupA≠1». (b)G is called hypercentral «iff each epimorphic imageH≠1 ofG hasZ(H)≠1». (c) the set of prime numbers which divide the orders of the torsion elements (≠1) ofG is called «the characteristic ofG». Baer has shown that each hypercyclic groupG is a subdirect product of hypercyclic groups of finite characteristic. In this note we will characterize hypercentral groups by abelian torsion groups of finite exponent.     

Some classes of groups with the weak minimality and maximality conditions for normal subgroups

This paper deals with groups satisfying the weak minimality (maximality) condition for normal subgroups and having an ascending series of normal subgroups whose factors are finite or Abelian of finite rank. It is proved that if G is such a group, then it contains a periodic hypercentral normal subgroup H satisfying the Min-G condition such that G/H is minimax and almost solvable.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1050–1056, August, 1990.