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ArticleOriginal scientific text

Title

Holomorph of generalized Bol loops II

Authors 1, 2

Affiliations

  1. Department of Mathematics, Faculty of Science, Obafemi Awolowo University, Ile Ife 220005, Nigeria
  2. Department of Mathematics, Federal College of Education, Osiele, Abeokuta 110101, Nigeria

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.

Keywords

ENG
generalized Bol loop, holomorph of a loop

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Discussiones Mathematicae - General Algebra and Applications
2015/35/1
Export to PBN, Opens in new tab
Pages:
59-78
Main language of publication
English
Received
2014-11-19
Accepted
2015-01-10
Published
2015

DOI: 10.7151/dmgaa.1234

Exact and natural sciences