Applications of conjunctive complex fuzzy subgroups to Sylow theory

Aneeza Imtiaz; Hanan Alolaiyan; Umer Shuaib; Abdul Razaq; Jia-Bao Liu; Aneeza Imtiaz; Hanan Alolaiyan; Umer Shuaib; Abdul Razaq; Jia-Bao Liu

doi:10.3934/math.2024003

AIMS Mathematics

2024, Volume 9, Issue 1: 38-54. doi: 10.3934/math.2024003

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Research article

Applications of conjunctive complex fuzzy subgroups to Sylow theory

1.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
2.
Department of Mathematics, King Saud University, Riyadh 145111, Saudi Arabia
3.
Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
4.
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China

Received: 20 August 2023 Revised: 01 November 2023 Accepted: 10 November 2023 Published: 24 November 2023
MSC : 03E72, 20N25, 08A72

Sylow's theorems are fundamental theorems in classical group theory that are of paramount importance. The extension of these theorems into diverse fuzzy contexts emerges as a compelling area of exploration. This study introduces the novel concept of the conjunctive complex fuzzy conjugate element within the conjunctive complex fuzzy subgroup of a group, elucidating numerous crucial properties of this concept. Additionally, it propounds the notion of the conjunctive complex fuzzy p-subgroup within the conjunctive complex fuzzy subgroup (CCFSG) and delineates various indispensable characteristics associated with this construct. Additionally, the paper formulates the conjunctive complex fuzzy version of the Cauchy theorem for finite groups. Lastly, it defines the concept of the conjunctive complex fuzzy Sylow p-subgroup for a finite group and conducts a generalization of Sylow's theorems within a conjunctive complex fuzzy environment.
- complex fuzzy subgroup,
- conjunctive complex fuzzy subgroup,
- conjunctive complex fuzzy Sylow p-subgroup
Citation: Aneeza Imtiaz, Hanan Alolaiyan, Umer Shuaib, Abdul Razaq, Jia-Bao Liu. Applications of conjunctive complex fuzzy subgroups to Sylow theory[J]. AIMS Mathematics, 2024, 9(1): 38-54. doi: 10.3934/math.2024003

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Abstract

Sylow's theorems are fundamental theorems in classical group theory that are of paramount importance. The extension of these theorems into diverse fuzzy contexts emerges as a compelling area of exploration. This study introduces the novel concept of the conjunctive complex fuzzy conjugate element within the conjunctive complex fuzzy subgroup of a group, elucidating numerous crucial properties of this concept. Additionally, it propounds the notion of the conjunctive complex fuzzy p-subgroup within the conjunctive complex fuzzy subgroup (CCFSG) and delineates various indispensable characteristics associated with this construct. Additionally, the paper formulates the conjunctive complex fuzzy version of the Cauchy theorem for finite groups. Lastly, it defines the concept of the conjunctive complex fuzzy Sylow p-subgroup for a finite group and conducts a generalization of Sylow's theorems within a conjunctive complex fuzzy environment.

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