Holomorph of generalized Bol loops II
Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 1, pp. 59-78
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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.
Keywords:
generalized Bol loop, holomorph of a loop
@article{DMGAA_2015_35_1_a5,
author = {Ja{\'\i}y\'eiọl\'a, T\`em{\'\i}tọ́pẹ́ and Popoola, Bolaji},
title = {Holomorph of generalized {Bol} loops {II}},
journal = {Discussiones Mathematicae. General Algebra and Applications},
pages = {59--78},
publisher = {mathdoc},
volume = {35},
number = {1},
year = {2015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGAA_2015_35_1_a5/}
}
TY - JOUR AU - Jaíyéiọlá, Tèmítọ́pẹ́ AU - Popoola, Bolaji TI - Holomorph of generalized Bol loops II JO - Discussiones Mathematicae. General Algebra and Applications PY - 2015 SP - 59 EP - 78 VL - 35 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMGAA_2015_35_1_a5/ LA - en ID - DMGAA_2015_35_1_a5 ER -
Jaíyéiọlá, Tèmítọ́pẹ́; Popoola, Bolaji. Holomorph of generalized Bol loops II. Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 1, pp. 59-78. http://geodesic.mathdoc.fr/item/DMGAA_2015_35_1_a5/