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arXiv · 1501.04620

Holomorph of generalized Bol loops

John Olushola Adéníran·Tèmítópé Gbóláhàn Jaíyéolá·Keheinde Adisa Ìdòwú
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Abstract

The notion of the holomorph of a generalized Bol loop and generalized flexible-Bol loop are characterized. With the aid of two self-mappings on the holomorph of a loop, it is shown that: the loop is a generalized Bol loop if and only if its holomorph is a generalized Bol loop; the loop is a generalized flexible-Bol loop if and only if its holomorph is a generalized flexible-Bol loop. Furthermore, elements of the Bryant Schneider group of a generalized Bol loop are characterized in terms of pseudo-automorphism, and the automorphisms gotten are used to build the holomorph of the generalized Bol loop.

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John Olushola Adéníran, Tèmítópé Gbóláhàn Jaíyéolá, Keheinde Adisa Ìdòwú. 2015-01-17. Holomorph of generalized Bol loops. https://arxiv.org/abs/1501.04620

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