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 embedde...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.展开更多
文摘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.
