Jordan-Hölder Theorem for Multigroups

Authors

  • Paul Augustine Ejegwa Department of Mathematics, Joseph Sarwuan Tarka University, P.M.B. 2373, Makurdi, Nigeria
  • Nasreen Kausar Department of Mathematics, Faculty of Arts and Sciences, Balikesir University 10145 Balikesir, Türkiye
  • Musa Adeku Ibrahim Department of Mathematics, Federal University Lokoja, Kogi State, Nigeria
  • Tonguc Cagin College of Business Administration, American University of the Middle East, Kuwait

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5889

Keywords:

Multiset, Multigroup, Order of multigroup, Simple multigroup, Maximal normal submultigroup, Normal series, Composition series

Abstract

Multigroup theory is the application of multisets to the theory of groups. Many group’s theoretic notions have been studied in multigroup theory, however, the ideas of maximal normal subgroup, simple group, normal series, composition series, and the Jordan-Hölder Theorem are yet to be investigated in multiset context. In this article, we define simple multigroup, maximal
normal submultigroup, normal series for multigroup, and composition series for multigroup with examples. With these concepts, we establish the Jordan-Hölder Theorem in multigroup theory. It is shown that every finite multigroup defined over a finite group has a composition series. In addition, it is established that every finite multigroup defined over a finite group has at least two composition series which are equivalent.

Downloads

Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Algebra

License

Copyright (c) 2025 Paul Augustine Ejegwa, Nasreen Kausar, Musa Adeku Ibrahim, Tonguc Cagin

Creative Commons License

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

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Jordan-Hölder Theorem for Multigroups. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5889. https://doi.org/10.29020/nybg.ejpam.v18i2.5889