On central loops and the central square property

TL;DR

This paper investigates the properties of central square C-loops, showing that isotopes of certain central square C-loops of exponent 4 retain their C-loop and A-loop structures.

Contribution

It demonstrates that isotopes of central square C-loops of exponent 4 are both C-loops and A-loops, advancing understanding of their algebraic structure.

Findings

Isotopes of central square C-loops of exponent 4 are C-loops.

Isotopes of these loops are also A-loops.

Representation sets of central square C-loops are characterized.

Abstract

The representation sets of a central square C-loop are investigated. Isotopes of central square C-loops of exponent 4 are shown to be both C-loops and A-loops.