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arXiv · 1510.05990

Holomorph of generalized Bol loops II

Tèmít\dóp\dé Gbóláhàn Jaíyéolá·B. A. Popoola
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Abstract

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 condition 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.

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Tèmít\dóp\dé Gbóláhàn Jaíyéolá, B. A. Popoola. 2015-10-16. Holomorph of generalized Bol loops II. https://doi.org/10.7151/dmgaa.1234

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