
TL;DR
This paper explores the properties and construction methods of D-loops, a class of loops with the antiautomorphic inverse property, highlighting differences from IP-loops and challenges in isotopy.
Contribution
It introduces new properties of D-loops, compares them with IP-loops, and presents methods for constructing D-loops from IP-loops, expanding understanding of their structure.
Findings
Smallest non-IP D-loop has six elements
D-loops are larger class than IP-loops
Isotopy does not preserve D-loop property
Abstract
-loops are loops with the antiautomorphic inverse property. The class of such loops is larger than the class of IP-loops. The smallest -loops which is not an IP-loop has six elements. We prove several basic properties of such loops and present methods of constructions of -loops from IP-loops. Unfortunately, a loop isotopic to a -loop may not be a -loop.
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Taxonomy
TopicsMathematics and Applications
