Coding Matrices for Wreath Products of Groups

Authors

  • Enoch Suleiman
    Department of Mathematics, Federal University Gashua, Yobe State, Nigeria
  • Ahmed A. Khammash
    Department of Mathematical Sciences, Umm Al-Qura University, Makkah, Saudi Arabia

Keywords:

Code, Ring of matrices, Group ring, Wreath product, Semi direct product, Matrix

Abstract

Wreath product, a powerful construction in group theory, has found extensive applications in various areas of mathematics and computer science. In this paper, we present a comprehensive analysis of coding matrices associated with wreath products. The coding matrices for the wreath product of two cyclic finite groups were given for the first time. It gives a generalization of the coding matrices for the semi-direct product. We found out that the coding matrix of wreath product really has the same shape as the one for semidirect product and gave the RW-matrix for the coding matrix. An example was showed to illustrate the assertions. Conditions were also given for different wreath products of cyclic groups and that gives different orders for the wreath products.

Dimensions

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Published

2023-07-11

How to Cite

Coding Matrices for Wreath Products of Groups. (2023). African Scientific Reports, 2(2), 114. https://doi.org/10.46481/asr.2023.2.2.114

Issue

Volume 2, Issue 2, August 2023

Section

Original Research
Copyright & Licensing

Copyright (c) 2023 Enoch Suleiman, Ahmed A. Khammash

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Coding Matrices for Wreath Products of Groups. (2023). African Scientific Reports, 2(2), 114. https://doi.org/10.46481/asr.2023.2.2.114

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