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黎曼流形上的幂零结构指什么？What is nilpotent structure on Riemannian manifold?

此外，本文还讨论了幂零指数的若干性质。Moreover, we shall discuss some properties of nilpotent exponents.

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线状李代数是一类重要的幂零李代数。Filiform Lie algebras are a class of special nilpotent Lie algebras.

通过对幂零矩阵的秩的研究，给出了一般方阵幂的秩的求法。By researching nilpotent matrix rank, a solution is obtained for general matrix power rank.

本文从矩阵的不同角度讨论了幂零矩阵的相关性质。This article discussed the nilpotent matrix related nature from the matrix different angle.

研究了有限生成的幂零群中元素的共轭分离问题。In this paper, conjugate separability problem in a finitely generated nilpotent group is researched.

研究了一类原点为三次幂零奇点的三次微分系统。A class of cubic differential system is studied in this paper, in which origin is nilpotent singular point.

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本文利用某些幂零子群的半正规性，讨论有限群的可解性，所得结果统一推广了王品超、赵耀庆的若干结果。In this paper, we investigate the solvability of finite groups by using some semi normal nilpotent subgroups.

本文较详细地描述了幂零矩阵子代数，并且获得了一些有趣的结果。In this note we describe explicitly the subalgebras of nilpotent matrices and obtain some interesting results.

本文给出了一般群分次环的分次幂零根的一个刻划。In this note, a characterization of the graded nilpotent radical of general group graded rings was established.

本文先给出幂零矩阵的定义，然后讨论了它的若干性质。This paper first presents the definition of nilpotent matrix and then moves on to discuss certain properties of them.

给出了所有准素子群的正规化子有素数幂指数的有限群的幂零长的界。The bounds of nilpotent lengths of finite groups with normalizers of primary subgroups having prime power indices are obtained.

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本文定义了有核半群的局部幂零根，并证明了与环相近的一些性质。In this paper, we define the local nilpotent radical of a semigroup having kernel and prove some properties which is similar to rings.

利用幂零矩阵的特性，给出了求一些特殊矩阵逆矩阵的简单方法。By the feature of the nilpotent matrix, the simple method for solving the inverse matrix of some special matrix is given in the present paper.

在高等代数中矩阵是研究问题很重要的工具，在讨论矩阵的乘法运算时给出了幂零矩阵的定义，但对其性质研究很少。However, the properties of nilpotent matrix have not been much explored although its definition is given in discussing the multiplication of matrix.

具体确定了一类中心为二维的三步幂零李代数的导子代数，得到了导子代数的一些性质，并证明了这类幂零李代数是可完备化幂零李代数。In this paper we explicitly determine the derivation algebras of a class of 3-step nilpotent Lie algebras, and obtain some properties of the derivation algebras.

第二部分利用有限域F_q上一类幂零阵的相似标准形，构作了一个笛卡尔认证码，并计算出该码的所有参数。Secondly, one construction of Cartesian authentication code from norm form of one class of nilpotent matrices over finite field is presented and its size parameters are computed.

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本文拟对后一类群作一较系统地刻划。我们先对该群类的极小反例的各种可能结构给以分析并确定，据此得出该群类的类似前二群类的一些性质。文?。The purpose of this paper is to determine construction of groups with nilpotent derived group, and then to obtain some properties similar to the class of nilpotent and supersoluber groups.

研究了线性无关的向量组在同一级幂零指数上的线性关系，得到幂零指数在线性空间的基向量上的分布规律。In this paper, the author researches the linear relation defined by a same nilpotent index in the independent vectors, obtains the distribution rule of the nilpotent indices on an arbitrary basis.