【摘要】：在本論文中,通過對(duì)態(tài)射及態(tài)射群的深入研究,定義了一種廣義態(tài)射和廣義態(tài)射群.首先探討了廣義態(tài)射和廣義態(tài)射群的一些基本性質(zhì),證明了態(tài)射群一定是廣義態(tài)射群,但廣義態(tài)射群不一定是態(tài)射群.這說明了廣義態(tài)射是態(tài)射概念的真正的推廣.其次,研究了廣義態(tài)射與群結(jié)構(gòu)之間的聯(lián)系,并給出了在群同構(gòu)下并不改變?nèi)旱膹V義態(tài)射性.得到了廣義態(tài)射如果為單同態(tài),則該廣義態(tài)射一定為滿同態(tài).進(jìn)一步舉例說明廣義態(tài)射的合成不一定是廣義態(tài)射.最后討論了p-群的廣義態(tài)射性并給出了p3階群的自同態(tài)為廣義態(tài)射的充要條件.
[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.
【學(xué)位授予單位】：青島大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O152

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本文編號(hào)：2405424