COMPLETENESS OF THE PARABOLIC SUBGROUPS OF PROJECTIVE ORTHOGONAL GROUPS

All parabolic subgroups and Borel subgroups of PΩ(2m 1, F) over a linear-able field F of characteristic 0 are shown to be complete groups, provided m > 3.     

Lefschetz Formulae for p -Adic Groups

Abstract In this paper, Lefschetz formulae for torus actions on p-adic groups are proven. These are similar to comparable formulae for real Lie groups. Applications lie in the realm of dynamical zeta functions.     

Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees II

Let G be a solvable group with five character degrees. Suppose that there is some prime p so that G/O ^p (G) is not Abelian. Also, assume that cd(G) contains a degree that is not divisible by p. Under these hypotheses, we show that the derived length of G is at most 4.     

Molecular programming of organogelators which can accept [60]fullerene by encapsulation

New porphyrin-based gelators bearing eight hydrogen-bond-forming amide groups at their periphery were synthesized. They acted as versatile gelators for aromatic solvents. SEM and TEM observations and X-ray crystallographic analysis established that they tend to aggregate into a two-dimensional sheet-like structure utilizing the intermolecular hydrogen-bonding interaction. In this structure the porphyrin-porphyrin π-π stacking interaction is not involved because of the energetically-predominant hydrogen-bonding interactions, keeping the space distance of 12.9 Å. Very interestingly, when C₆₀ was added, the morphology was transformed to a one-dimensional fibrous structure, which can enjoy a porphyrin-C₆₀-porphyrin interaction. This multicapsular structure having porphyrin-based compartments for hosting C₆₀ was further characterized by XRD, EPR of a Cu(II) analogue, and the theoretical calculation. Thus, this paper presents a new concept, ‘molecular recognition in gel’, which is effective for the weak host-guest interaction.     

Integrated Groups and Smooth Distribution Groups

In this paper, we prove directly that α-times integrated groups define algebra homomorphisms. We also give a theorem of equivalence between smooth distribution groups and α-times integrated groups.     

Rigidity of Branch Groups Acting on Rooted Trees

Automorphisms of groups acting faithfully on rooted trees are studied. We find conditions under which every automorphism of such a group is induced by a conjugation from the full automorphism group of the rooted tree. These results are applied to known examples such as Grigorchuk groups, Gupta–Sidki group, etc.     

有限局部环Z/2\+kZ上斜对称矩阵标准形和伪辛群的阶

设R=Z/2\+kZ(k>1)是\{2\}[TX-]为非单位的有限局部环. 该文首先确定了R上斜对称矩阵标准形. 设G\+m\-p(R,H)={P∈GL\-m(R)|PHP′=H}是由矩阵H确定的伪辛群,其中H=[JB((][HL(2]0[]I\+\{(v)\}\=-I\+\{(v)\}[]0[HL)][JB))]Δ，Δ=[JB((][HL(2]\{2\}[TX-]\+\{k-1\}[]\{1\}[TX-]\=-\{1\}[TX-][]0[HL)][JB))]. 其次,计算了伪辛群G\+m\-P(R,H)的阶|G\+m\-P(R,H)|.     

The intertwining lifting theorem for ordered groups

Sz.-Nagy's dilation theorem for a contraction on a Hilbert space has been extended by Mlak to the case of a contraction semigroup whose indices are the positive elements of a totally ordered discrete group. We generalize to this case the intertwining lifting theorem of Sz.-Nagy and Foias. Some previous interpolation results on ordered groups are obtained as consequences.     

带作用的群系的临界结构

在本文中，我们讨论了带作用群的群系的临界结构，给出了处理允许某些作用群的群的问题的一般方法，作为应用，我们特别给出了关于幂零群及ｐ－幂零群的一些结果。     

Selectively protected galactose derivatives for the synthesis of branched oligosaccharides

Synthesis and characterization of several new anomerically pure galactose derivatives, based on simple and effective protective group manipulations of benzyl β-d-galactopyranoside, are reported. The monosaccharides described contain selectively protected/deprotected hydroxyl functionalities at their 1,2,3,4- and 6-positions rendering them useful as building blocks for construction of branched oligosaccharides.