Bruck decomposition for endomorphisms of quasigroups
P. T. Nagy, P. Plaumann

TL;DR
This paper explores the structure of certain quasigroups using Bruck's extension method, focusing on cases where the endomorphism map's image forms a group, and characterizes these quasigroups within specific varieties.
Contribution
It introduces a characterization of quasigroups with endomorphic $e$-maps via Bruck decomposition, expanding understanding of their algebraic structure.
Findings
Constructs examples of LF-quasigroups with group images of $e$
Characterizes quasigroups where $e$ is an endomorphism
Describes subvarieties with group images of $e$
Abstract
In the year 1944 R. H. Bruck has described a very general construction method which he called the extension of a set by a quasigroup. We use it to construct a class of examples for LF-quasigroups in which the image of the map is a group. More generally, we consider the variety of quasigroups which is defined by the property that the map is an endomorphism and its subvariety where the image of the map is a group. We characterize quasigroups belonging to these varieties using their Bruck decomposition with respect to the map .
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 · Optics and Image Analysis
