On Jordan-Hölder Theorem under Intuitionistic Fuzzy Groups

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, Turkiye
  • Tonguc Cagin College of Business Administration, American University of the Middle East, Kuwait

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5908

Keywords:

ntuitionistic fuzzy groups, Intuitionistic fuzzy subgroups, simple intuitionistic fuzzy groups, normal series for intuitionistic fuzzy groups, composition series for intuitionistic fuzzy groups

Abstract

The theory of intuitionistic fuzzy groups is an algebraic structure derivable from the utilization of groups in intuitionistic fuzzy sets. Many notions in group theory have been presented in intuitionistic fuzzy group theory. However, concepts like simple group, maximal normal subgroup, normal series, composition series, and the Jordan-Hölder Theorem are open problems in intuitionistic fuzzy group theory. Hence, this paper defines simple intuitionistic fuzzy groups, maximal normal intuitionistic fuzzy subgroups, normal series for intuitionistic fuzzy groups, and composition series for intuitionistic fuzzy groups with illustrations. In addition, the Jordan-Hölder Theorem in intuitionistic fuzzy group theory is verified. It is shown that every intuitionistic fuzzy group of a finite group possesses a composition series, and any two composition series for an intuitionistic fuzzy group of a finite group are equivalent.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Algebra

License

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

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How to Cite

On Jordan-Hölder Theorem under Intuitionistic Fuzzy Groups. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5908. https://doi.org/10.29020/nybg.ejpam.v18i2.5908