The Structure of F-Quasigroups
Tom\'a\v{s} Kepka, Michael K. Kinyon, and J. D. Phillips
TL;DR
This paper characterizes the structure of F-quasigroups by showing they have Moufang loop isotopes that are central products of their nucleus and Moufang center, solving a longstanding open problem since 1967.
Contribution
It provides a complete characterization of F-quasigroups' structure through their Moufang loop isotopes, addressing a problem posed by Belousov.
Findings
Every F-quasigroup has a Moufang loop isotope.
The Moufang loop isotope is a central product of the nucleus and Moufang center.
The structure of the F-quasigroup can be understood via its associated Moufang loop.
Abstract
We solve a problem of Belousov which has been open since 1967: to characterize the loop isotopes of F-quasigroups. We show that every F-quasigroup has a Moufang loop isotope which is a central product of its nucleus and Moufang center. We then use the loop to reveal the structure of the associated F-quasigroup.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematics and Applications · graph theory and CDMA systems · History and Theory of Mathematics