Research article

Applications of conjunctive complex fuzzy subgroups to Sylow theory

  • 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.

    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

    Related Papers:

  • 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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