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
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• 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.