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1·By, we prove that a separative Abelian regular ring is an APT ring.

由，还证明了分离的阿贝尔正则环是APT环。

2·The ellipse rotating symmetric group is proposed, which is an Abelian group.

提出椭圆旋转对称群，它是一个单参数阿贝尔群。

3·In this paper, the finite non-nilpotent group with every non-abelian subgroup being subnormal is investigated.

研究了每一非交换子群皆为次正规的有限非幂零群的结构。

4·Let R be an abelian ring ( all idempotents of R lie in the center of R), and A be an idempotent matrix over R.

设R是一阿贝尔环（R的所有幂等元都在中心里），A是R上的一幂等阵。

5·For the latter, we obtain the linear estimation of the number of isolated zeros of the corresponding Abelian integral.

对于另一类得到了其相应的阿贝尔积分的孤立零点的估计。

6·Concerning the Abelian groups and solvable groups, the researches on CI-properties had rather thorough results until now.

到目前为止，对于交换群和可解群，CI -性的研究已有了相当彻底的结果。

7·In this paper, we give a conjugacy-class-length characterization of finite minimal non-abelian groups and establish some related results.

文中，我们给出了有限极小非abel群的一个共轭类长——刻画并建立某些相关的结果。

8·Using the notion of coefficient matrix and maximal element. We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.

利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。

9·In the last section, namely 3.4, we mainly discuss how Abelian subgroups influent the solvability of finite groups, so we obtain some sufficient conditions of solvable groups.

本文第四部分3.4，主要讨论了交换子群对有限群可解性的影响，得到了有限群可解的若干充分条件。

10·In the first section, namely 3.1, we obtained some description of the structure of some finite groups whose centralizers or normalizers of Abelian subgroups satisfy some conditions.

在第一部分3.1中，给出了若干由交换子群的中心化子或正规化子满足的条件所确定的有限群的结构描述。

(1)abelian group阿贝尔群；[数]交换群