Holomorph of generalized Bol loops II

Tèmítọ́pẹ́ Gbọ́láhàn Jaíyéiọlá; Bolaji Ajibola Popoola

Discussiones Mathematicae - General Algebra and Applications (2015)

  • Volume: 35, Issue: 1, page 59-78
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Tèmítọ́pẹ́ Gbọ́láhàn Jaíyéiọlá, and Bolaji Ajibola Popoola. "Holomorph of generalized Bol loops II." Discussiones Mathematicae - General Algebra and Applications 35.1 (2015): 59-78. <http://eudml.org/doc/270737>.

@article{Tèmító2015,
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 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.},
author = {Tèmítọ́pẹ́ Gbọ́láhàn Jaíyéiọlá, Bolaji Ajibola Popoola},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {generalized Bol loop; holomorph of a loop},
language = {eng},
number = {1},
pages = {59-78},
title = {Holomorph of generalized Bol loops II},
url = {http://eudml.org/doc/270737},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Tèmítọ́pẹ́ Gbọ́láhàn Jaíyéiọlá
AU - Bolaji Ajibola Popoola
TI - Holomorph of generalized Bol loops II
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2015
VL - 35
IS - 1
SP - 59
EP - 78
AB - 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.
LA - eng
KW - generalized Bol loop; holomorph of a loop
UR - http://eudml.org/doc/270737
ER -

References

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