Holomorph of generalized Bol loops
Group Theory
2015-01-21 v1
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.
Keywords
Cite
@article{arxiv.1501.04620,
title = {Holomorph of generalized Bol loops},
author = {John Olushola Adéníran and Tèmítópé Gbóláhàn Jaíyéolá and Keheinde Adisa Ìdòwú},
journal= {arXiv preprint arXiv:1501.04620},
year = {2015}
}
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