Advances in Pure Mathematics

Volume 11, Issue 2 (February 2021)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

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On Some Embedment of Groups into Wreath Products

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DOI: 10.4236/apm.2021.112007    282 Downloads   1,032 Views  Citations

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.

Share and Cite:

Suleiman, E. and Audu, M. (2021) On Some Embedment of Groups into Wreath Products. Advances in Pure Mathematics, 11, 109-120. doi: 10.4236/apm.2021.112007.

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