Homology of Nilpotent Subalgebras of the Lie Superalgebra K(1,1).3

We calculate the dimensions of the second homology groups with trivial coefficients of nilpotent subalgebras of the Lie superalgebra , which is the natural superanalog of the Witt algebra. The proof is based on direct calculations of the rank of the differential. As an application, we find deformations of the maximal nilpotent subalgebra in .     

A Remark on Subgroup Separability in the Class of Finite π-Groups

We prove that if a group G is residually , then for every -subgroup of the group G, the set of -roots from this subgroup is a -separable -subgroup.     

Wreath Products and Universal Equivalence

We consider the question of preservation of universal equivalence for the cartesian and direct wreath products of lattice-ordered groups and groups. We prove that the basic rank is infinite of the quasivariety of torsion-free nilpotent groups of nilpotence length c (c2)     

（n-3）-Filiform李代数的极大环面

求出了（n-3）-filiform李代数的极大环面，并证明了（n-3）-filiform李代数是可完备化的．     

一类特殊的无限非正则p-群

利用有限正则p-群和局部幂零群的理论,得到:如果G是可解的非正则p-群,且G的每一个无限真子群是正则的,那么群G是秩为p-1的可除阿贝尔群被循环群的扩张.     

一类新的极小谱任意符号模式

若给定任意一个$n$次首一实系数多项式$f(\lambda)$,都存在一个实矩阵$B\in Q(A)$, 使得$B$的特征多项式为$f(\lambda)$,则称$A$为谱任意符号模式. 如果一个谱任意符号模式的任意非零元被零取代后所得到的符号模式不是谱任意,那么这个谱任意符号模式称为极小谱任意符号模式.本文证明一类极小谱任意符号模式.     

所有子群皆交换或正规的有限群

本文研究所有子群皆交换或正规的有限群. 我们获得了非幂零的情形的一个特征刻画, 也给出了幂零情形的一些性质.     

一类具幂零奇点的五次系统中心条件及极限环分支

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 8 quasi Lyapunov constants are deduced. As a result, the necessary and sufficient conditions to have a center are obtained. The fact that there exist 8 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems.     

一类广义幂零群

This paper considers such a group G which possesses nontrivial proper subgroups H 1 ,H 2 such that any proper subgroup of G not contained in H 1 ∪ H 2 is p-closed and obtains that if G is soluble,then the number of prime divisors contained in ｜G｜ is 2,3 or 4;if not,then it has a form x N where N/Φ（N） is a non-abelian simple group.Then the structure of such a group is determined for p = 2,H 1 = H 2 under some conditions.