On Some Embedment of Groups into Wreath Products  

作　　者：Enoch Suleiman Muhammed Salihu Audu Enoch Suleiman;Muhammed Salihu Audu(Department of Mathematics, Federal University Gashua, Yobe State, Nigeria;Department of Mathematics, University of Jos, Jos, Nigeria)

机构地区：[1]Department of Mathematics, Federal University Gashua, Yobe State, Nigeria [2]Department of Mathematics, University of Jos, Jos, Nigeria

出　　处：《Advances in Pure Mathematics》2021年第2期109-120,共12页理论数学进展（英文）

摘　　要：In this paper, we showed how groups are embedded into wreath products, we gave a simpler proof of the theorem by Audu (1991) (see <a href="#ref1">[1]</a>), also proved that a group can be embedded into the wreath product of a factor group by a normal subgroup and also proved that a factor group can be embedded inside a wreath product and the wreath product of a factor group by a factor group can be embedded into a group. We further showed that when the abstract group in the Universal Embedding Theorem is a <em>p</em>-group, cyclic and simple, the embedding becomes an isomorphism. Examples were given to justify the results.In this paper, we showed how groups are embedded into wreath products, we gave a simpler proof of the theorem by Audu (1991) (see <a href="#ref1">[1]</a>), also proved that a group can be embedded into the wreath product of a factor group by a normal subgroup and also proved that a factor group can be embedded inside a wreath product and the wreath product of a factor group by a factor group can be embedded into a group. We further showed that when the abstract group in the Universal Embedding Theorem is a <em>p</em>-group, cyclic and simple, the embedding becomes an isomorphism. Examples were given to justify the results.

关 键 词：Wreath Product Direct Product HOMOMORPHISM Embedding p-Group Cyclic Simple 

分 类 号：O17[理学—数学]