幂零群

This paper researches linear maps preserving orthogonality,obtains the linear maps preserving othrogonality,it is either a rank -declining or rank -keeping map or a map with nilpotent element in its codomain.

利用分块成向量的方法证明了MnMn(F为域F上所有n×n矩阵构成的乘法半群上的n×n拟正交矩阵组至多含有n个矩阵，利用方程组的解的理论证明了Mn中与给定矩阵A构成两两拟正交矩阵组的矩阵个数不超过n-Rank+1，从而得到Mn上保持拟正交性的线性映射φ要么是降秩的或者保秩的映射，要么φ的值域中含有幂零元。

In Chapter one, the theory of irreducible unitary representations on two-step nilpotent Lie groups is introduced.

在第一章中，首先介绍了二步幂零Lie群上的不可约酉表示理论。

Integrability of some subbundles and geometric structuresin case of integrable,isometry groups on the〓-H-type groups.

在第二章中，我们构造并且研究了二步齐性幂零流形的另一类〓型群的几何性质。

The nilpotency of finite groups was studied by the properties of semidirect product,and some good results were got.

通过半直积的性质来研究有限群的幂零性，并得到一些好的结果。

In [10,13], the authors gave some conditions on which a group is nilpotent by c- normality of subgroups.

文献[10，13]利用子群的c-正规性给出了一个群是幂零一些条件。

Nilpotent and solvable Lie groups with left-invariant Riemannian metrics play aremarkable role in Riemannian geometry.

在黎曼几何中，带有左不变黎曼度量的幂零和可解李群具有重要作用。

On the basis, three equivalent statements are obtained. Let S be a semigroup with left central idempotents, then (1) S is a quasi-right semigroup;(2) S is a quasi-completely regular, and RegS is an ideal;(3) S is a nil-extension of strong semilattice of right semigroup.

在此基础上得到了3个等价命题：若S为具有左中心幂等元半群，则(1) S为拟右半群；(2) S为拟完全正则的，RegS为S的理想；(3) S为右群强半格的诣零理想扩张。

By using properties of quasi-regular semigroups and left central idempotents, some statements are proved. Let S be a quasi-right semigroup, then (1) S is a quasi-completely regular semigroup;(2) RegS is a completely regular semigroup;(3) R(superscript *) is the smallest semilattice congruence on S;(4) Each R-class T(subscript α) on RegS is a right group;(5) T(subscript α)G(subscript α)×E(subscript α), where G(subscript α) is a group, E(subscript α) is a right zero semigroup.

利用拟正则半群和左中心幂等元的性质，证明了S为拟右半群时，(1) S为拟完全正则半群；(2) RegS为完全正则半群；(3) R为S上的最小半格同余；(4) RegS上的每个R-类T为右群；(5) TG×E，其中G为群，E为右零半群。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。