TITLE:
On Some Embedment of Groups into Wreath Products
AUTHORS:
Enoch Suleiman, Muhammed Salihu Audu
KEYWORDS:
Wreath Product, Direct Product, Homomorphism, Embedding, p-Group, Cyclic, Simple
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.11 No.2,
February
5,
2021
ABSTRACT: In this paper, we showed how groups are embedded into wreath products, we gave a simpler proof of the theorem by Audu (1991) (see [1]), 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 p-group, cyclic and simple, the embedding becomes an isomorphism. Examples were given to justify the results.