一类新的具有某种性质的自同态
发布时间：2019-01-09 09:12
【摘要】：在本论文中,通过对态射及态射群的深入研究,定义了一种广义态射和广义态射群.首先探讨了广义态射和广义态射群的一些基本性质,证明了态射群一定是广义态射群,但广义态射群不一定是态射群.这说明了广义态射是态射概念的真正的推广.其次,研究了广义态射与群结构之间的联系,并给出了在群同构下并不改变群的广义态射性.得到了广义态射如果为单同态,则该广义态射一定为满同态.进一步举例说明广义态射的合成不一定是广义态射.最后讨论了p-群的广义态射性并给出了p3阶群的自同态为广义态射的充要条件.
[Abstract]:In this paper, a generalized morphism and a generalized morphism group are defined by studying morphism and morphism groups in depth. Firstly, some basic properties of generalized morphisms and generalized morphisms are discussed. It is proved that morphisms must be generalized morphisms, but generalized morphisms are not necessarily morphisms. This shows that the generalized morphism is a true generalization of the concept of morphism. Secondly, the relation between generalized morphism and group structure is studied, and the generalized morphism of group is not changed under group isomorphism. It is obtained that if the generalized morphism is a single homomorphism, the generalized morphism must be a full homomorphism. A further example is given to illustrate that the composition of generalized morphism is not necessarily a generalized morphism. Finally, the generalized morphisms of p- groups are discussed and the necessary and sufficient conditions for the endomorphism of groups of order p3 to be generalized morphisms are given.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152
本文编号：2405424
[Abstract]:In this paper, a generalized morphism and a generalized morphism group are defined by studying morphism and morphism groups in depth. Firstly, some basic properties of generalized morphisms and generalized morphisms are discussed. It is proved that morphisms must be generalized morphisms, but generalized morphisms are not necessarily morphisms. This shows that the generalized morphism is a true generalization of the concept of morphism. Secondly, the relation between generalized morphism and group structure is studied, and the generalized morphism of group is not changed under group isomorphism. It is obtained that if the generalized morphism is a single homomorphism, the generalized morphism must be a full homomorphism. A further example is given to illustrate that the composition of generalized morphism is not necessarily a generalized morphism. Finally, the generalized morphisms of p- groups are discussed and the necessary and sufficient conditions for the endomorphism of groups of order p3 to be generalized morphisms are given.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152
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3 李欣;海进科;;关于态射的一个注记[J];青岛大学学报(自然科学版);2012年01期
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