Construction of groups with triality and their corresponding code loops
Rosemary Miguel Pires, Alexandre Grishkov, Rodrigo Lucas Rodrigues, and Marina Rasskazova

TL;DR
This paper generalizes the construction of code loops using groups with triality, demonstrating how to build specific nilpotent groups and Moufang loops with particular properties related to code loops.
Contribution
It introduces a new method for constructing groups with triality and associated Moufang loops, extending previous work to a broader class of loops and groups.
Findings
Constructed nilpotent groups of class 3 with triality
Proved Moufang loops are free loops in a specific variety
Embedded free loops into direct products of smaller loops
Abstract
We generalize the global construction of code loops introduced by Nagy, which is based on the connection between Moufang loops and groups with triality. This follows from the construction of a nilpotent group of class 3 with triality and generators, based on embeddings of into direct products of copies of . In the finite case, where is a group such that with and , we prove that the corresponding Moufang loop is the free loop with generators in the variety generated by code loops. The result depends on a construction similar to that of , namely, embedding into direct products of copies of , the free code loop associated with .
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 · Finite Group Theory Research
