Locally nilpotent groups with the min−∞−n condition

The study of locally nilpotent groups with the weak minimality condition for normal subgroups, the min^––n condition, is continued. The following results are obtained.THEOREM 1. A locally nilpotent group with the min^––n condition is countable.THEOREM 2. If G is a locally nilpotent group with the min^––n condition whose periodic part is nilpotent and the orders of the elements of the periodic part are bounded in the aggregate, then G=t(G)A, where the subgroup A is minimax.THEOREM 3. Suppose G is a locally nilpotent group with the min^––n condition and T is its periodic part. If T is nilpotent and G/T is Abelian, then G=TA, where the subgroup A is minimax.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 340–346, March, 1990.     

On some groups all subgroups of which are nearly pronormal

A subgroup H of a group G is called nearly pronormal in G if, for every subgroup L of the group G that contains H, the normalizer N _L (H) is contranormal in L. We prove that if G is a (generalized) solvable group in which every subgroup is nearly pronormal, then all subgroups of G are pronormal. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1331–1338, October, 2007.     

氢原子在过渡金属修饰的Mg(0001)面扩散的第一性原理研究

基于密度泛函理论(DFY)的第一性原理计算方法,对氢原子在过渡金属(Sc、Ti、Cr、Mn、Fe、Co、Ni、Cu、V、Zn)修饰的Mg(0001)表面扩散性能进行了研究.研究发现过渡金属元素Sc、Ti、V、Cr、Mn、Fe、Co、Ni和Cu选择替代在镁表面第二层稳定,而Zn则选择替代在第一层稳定.当镁表面掺杂Zn和Cu时,氢原子选择停留在表面稳定;当掺杂Sc、Ti、V、Cr、Mn、Fe、Co和Ni时,氢原子选择进入镁块体内部.值得一提的是氢原子通过从过渡金属顶部通道扩散进入镁块体内部的势垒大大降低,笔者用差分电荷密度分析后发现氢原子与过渡金属原子成键使扩散势垒降低.当氢原子进入镁块体内部后靠近Sc、Ti、V、Cu和Zn原子时,将与这些过渡金属原子成键,从而阻碍了氢原子继续向内部扩散;而氢原子靠近Cr、Mn、Fe、Co、Ni原子时,选择离开过渡金属从而促进了氢原子向块体内扩散,可以大幅改善镁基储氢材料的吸氢动力性能.     

Groups with Bounded Chernikov Conjugate Classes of Elements

We consider BCC-groups, that is groups G with Chernikov conjugacy classes in which for every element x G the minimax rank of the divisible part of the Chernikov group G/C _G(x ^G) and the order of the corresponding factor-group are bounded in terms of G only. We prove that a BCC-group has a Chernikov derived subgroup. This fact extends the well-known result due to B. H. Neumann characterizing groups with bounded finite conjugacy classes (BFC-groups).     

Groups with subnormality for all subgroups that are not finitely generated

Summary We characterize the groups given in the title in the case of locally finite, locally nilpotent and radical groups.

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Sunto I gruppi con tutti i sottogruppi nonfinitamente generati subnormali sono caratterizzati nella classe dei gruppi localmente finiti, localmente nilpotenti e radicali.

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This work was carried out while the second author visited the University of Würzburg with the aid of Deutsche Forschungsgemeinschaft (DFG). The second author is grateful to DFG for making this visit possible and to Mathematisches Institut Würzburg for the hospitality he enjoyed.     

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.     

Prenatal stress and subsequent exposure to chronic mild stress influence dendritic spine density and morphology in the rat medial prefrontal cortex

Background  

Both prenatal stress (PS) and postnatal chronic mild stress (CMS) are associated with behavioral and mood disturbances in humans and rodents. The aim of this study was to reveal putative PS- and/or CMS-related changes in basal spine morphology and density of pyramidal neurons in the rat medial prefrontal cortex (mPFC).