An extension formula for right Bol loops arising from Bol reflections

TL;DR

This paper introduces a new extension formula for right Bol loops, providing conditions for the extension to retain the right Bol property and analyzing key invariants and structural aspects.

Contribution

It presents a novel extension formula for right Bol loops and characterizes the invariants and structural properties of the resulting loops.

Findings

Derived necessary and sufficient conditions for right Bol extensions

Described the invariants: right multiplication group, nuclei, and center

Analyzed the core as an involutory quandle and its structure group

Abstract

We study a new extension formula for right Bol loops. We prove the necessary or sufficient conditions for the extension to be right Bol. We describe the most important invariants: right multiplication group, nuclei, and center. We show that the core is an involutory quandle which is the disjoint union of two isomorphic involutory quandles. We also derive further results on the structure group of the core of the extension.