Composition Series and Jordan-Holder Theorem under Fuzzy Multigroups

Authors

  • Paul Augustine Ejegwa Department of Mathematics, Joseph Sarwuan Tarka University, 970101, Makurdi, Nigeria
  • Nasreen Kausar Department of Mathematics, Faculty of Arts and Science, Balikesir University, 10145, Balikesir, Turkey
  • Tonguc Cagin College of Business Administration, American University of the Middle East, 15453, Egaila, Kuwait
  • Aseel Smerat Faculty of Educational Sciences, Al-Ahliyya Amman University, 19328, Amman, Jordan & Department of Biosciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, 602105, Chennai, India

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i2.7163

Keywords:

fuzzy multigroup, fuzzy multiset, order of fuzzy multigroup, simple fuzzy multigroup, maximal normal fuzzy submultigroup, normal series, composition series, Jordan-Holder Theorem

Abstract

The theory of fuzzy multigroups is an algebraic structure derivable from the application of fuzzy multisets to groups. Various concepts in group theory have been considered in fuzzy multigroup theory. However, simple group, maximal normal subgroup, normal series, composition series, and the Jordan-H\"{o}lder Theorem are open problems in fuzzy multigroup theory. Hence, this paper defines simple fuzzy multigroups, maximal normal fuzzy submultigroups, normal series for fuzzy multigroups, and composition series for fuzzy multigroups with illustrations. In addition, the Jordan-H\"{o}lder Theorem in fuzzy multigroup theory is established. We show that each finite fuzzy multigroup of a finite group possesses a composition series, and also prove that two composition series for a finite fuzzy multigroup of a finite group are comparable.

References

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Published

2026-07-28

Issue

Vol. 19 No. 2: (April 2026)

Section

Algebra

License

Copyright (c) 2026 Paul Augustine Ejegwa, Nasreen Kausar, Tonguc Cagin, Aseel Smerat

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How to Cite

Composition Series and Jordan-Holder Theorem under Fuzzy Multigroups. (2026). European Journal of Pure and Applied Mathematics, 19(2), 7163. https://doi.org/10.29020/nybg.ejpam.v19i2.7163