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.
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)
