Some Simplicial Complexes of Universal Osborn Loops

Abstract

A loop is shown to be a universal Osborn loop if and only if it has a particular simplicial complex. A loop is shown to be a universal Osborn loop and obeys two new identities if and only if it has another particular simplicial complex. A universal Osborn loop and four of its isotopes are shown to form a rectangular pyramid in a 3-dimensional space.

Keywords

• osborn loops
• universality
• left universality
• right universality