Application of t-intuitionistic fuzzy subgroup to Sylow theory

• Published in: Heliyon Vol. 9; no. 9; p. e19822
• Main Authors: Latif, Laila, Shuaib, Umer
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2023; Elsevier
• Subjects: Subgroup ([formula omitted]); Subgroup (t−IFSylp); t-Intuitionistic fuzzy conjugate element; t-Intuitionistic fuzzy conjugate subgroup (t-[formula omitted]); t-Intuitionistic fuzzy conjugate subgroup (t-IFCSG); t-Intuitionistic fuzzy subgroup (t-[formula omitted]); t-Intuitionistic fuzzy subgroup (t-IFSG); t-Intuitionistic fuzzy Sylow[formula omitted]; t-Intuitionistic fuzzy Sylowp; t-Intuitionistic fuzzy[formula omitted] Subgroup; t-Intuitionistic fuzzyp− Subgroup; t-Intuitionistic fuzzy conjugate element; Subgroup (t−IFSylp); t-Intuitionistic fuzzy Sylowp; t-Intuitionistic fuzzyp− Subgroup; t-Intuitionistic fuzzy conjugate subgroup (t-IFCSG); t-Intuitionistic fuzzy subgroup (t-IFSG)
• ISSN: 2405-8440; 2405-8440
• DOI: 10.1016/j.heliyon.2023.e19822

In this paper, we define the notion of a t-intuitionistic fuzzy conjugate element and determine the t-intuitionistic fuzzy conjugacy classes of a t-intuitionistic fuzzy subgroup. We propose the idea of a t-intuitionistic fuzzy p− subgroup and prove the t-intuitionistic fuzzy version of the Cauchy theorem. In addition, we present the idea of a t-intuitionistic fuzzy conjugate subgroup and investigate various fundamental algebraic characteristics of this notion. Furthermore, we provide the idea of the t-intuitionistic fuzzy Sylow p− subgroup and prove the t-intuitionistic fuzzification of Sylow's theorems.