Abnormal,Pronormal, Contranormal,and Carter Subgroups in Some Generalized Minimax Groups

ABSTRACT

Some properties of abnormal and pronormal subgroups in generalized minimax groups are considered. For generalized minimax groups (not only periodic) whose locally nilpotent residual is nilpotent and satisfies Min-G the existence of Carter subgroups and their conjugations have been proven. Some generalizations of results of J. Rose on abnormal and contranormal subgroups have been also obtained.     

Locally nilpotent linear groups with restrictions on their subgroups of infinite central dimension

Let F be a field and V a vector space over F. If G is a subgroup of GL(V, F), then we define the central dimension of G (denoted by centdim _F G) as the F-dimension of the factor-space V/C _V (G). In this paper, we continue the study of locally nilpotent linear groups satisfying the weak minimal or the weak maximal condition on their subgroups of infinite central dimension started in Kurdachenko et al. (Publ Mat 52:151–169, 2008). Supported by Proyecto MTM2007-60994 of Dirección General de Investigación MEC (Spain).     

Modules over Group Rings with Certain Finiteness Conditions

We study modules over the group ring DG all proper submodules of which are finitely generated as D-modules.     

含铁磁耦合Ni3单元的均苯三甲酸桥联双层镍(II)配合物

使用均苯三甲酸与碳酸镍在水热条件下反应得到了一例新的二维双层Ni(II)配位聚合物Ni3(BTC)2(μ-H2O)26H2O。二维层包含syn-syn羧酸桥和水桥连接的三核Ni3单元,进一步用均苯三甲酸上的苯环连接成二维层状结构。磁性研究表明,相邻Ni2+离子间存在弱的铁磁耦合作用。水桥连镍离子的桥联键角为122.8(3)deg,所以通过该水桥镍离子间应该呈现反铁磁耦合。因此,实验结果证明了syn-syn羧酸桥传递铁磁耦合,而且铁磁耦合大于反铁磁作用,最终配合物呈弱的铁磁耦合。基于本工作和文献报道的含syn-syn 羧酸混合桥联镍配合物的磁性,我们总结出下面结论：Ni–O–C–O–Ni的共面性与否决定了配合物的磁性。共面性好的Ni–O–C–O–Ni导致中等强度的反铁磁耦合,而共面性差会消弱反铁磁作用,甚至出现由反铁磁变为铁磁耦合。标题配合物中羧酸桥所传递的铁磁性可能就归因于Ni–O–C–O–Ni的不共平面性。因此,与含羧酸桥的混合桥联双核铜(II)配合物类似,轨道补偿效应(the orbital complementary effect (OCE))对于解释水/羧酸混合桥联镍(II)配合物的磁性也同样适用。     

Coherent Dynamics of Direct-Current-Driven Quantum-Dot-Array with Two Time-Dependent Embedded Impurities

The coherent dynamics of dc-driven quantum-dot array with two embedded time-dependent impurities is investigated, the exact crossings and avoided crossings in the quasienergies are associated with the evolution dynamics of the electron by the introduction of the envelope lines of the site＇s maximum returning probability. Through a perturbative scheme, the time-dependent Hamiltonian is replaced by an equivalent static one, whose structure reveals the new quantum tunnelling mechanism in the time-periodic driving system and sheds light on the alternative interpretation of dynamic localization and delocalization.