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On the isotopic characterizations of generalized Bol loops

  • Adeniran, John Olusola [1] ; Jaiyeola, Temitope Gbolahan [2] ; Idowu, Kehinde Adisa
    1. [1] Federal University of Agriculture

      Federal University of Agriculture

      Nigeria

    2. [2] Obafemi Awolowo University

      Obafemi Awolowo University

      Nigeria

  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 4, 2022, págs. 805-823
  • Idioma: inglés
  • DOI: 10.22199/issn.0717-6279-4581
  • Enlaces
  • Resumen

    • In this study, the notion of isotopy of generalized Bol loop is characterized. A loop isotope of a σ-generalized Bol loop is shown to be a σ'-generalized Bol loop if σ' fixes its (isotope) identity element where σ' is some conjugate of σ. A loop isotope of a σ-generalized Bol loop is shown to be a σ'-generalized Bol loop if and only if the image of the isotope’s identity element under σ' is right nuclear (where σ' is some conjugate of σ). It is shown that a generalized Bol loop can be constructed using a group and a subgroup of it. A right conjugacy closed σ-generalized Bol loop is shown to be a σ-generalized right central loop.

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