Holomorph of generalized Bol loops II

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...

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Veröffentlicht in:arXiv.org 2015-10
Hauptverfasser: Tèmít\dóp\dé Gbóláhàn Jaíyéolá, Popoola, B A
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1510.05990