Geodesic
Holomorph of generalized Bol loops II
Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 1, pp. 59-78

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The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the loop are right (middle) regular. The holomorph of a RIPL is shown to be a GBL if and only if the loop is a GBL and some elements of the loop are right (middle) nuclear. Necessary and sufficient conditions for the holomorph of a RIPL to be a Bol loop are deduced. Some algebraic properties and commutative diagrams are established for a RIPL whose holomorph is a GBL.
Keywords: generalized Bol loop, holomorph of a loop 
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Jaíyéiọlá, Tèmítọ́pẹ́; Popoola, Bolaji. Holomorph of generalized Bol loops II. Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 1, pp. 59-78. http://geodesic.mathdoc.fr/item/DMGAA_2015_35_1_a5/