# Moufang Theorem for a variety of local non-Moufang loops

## TL;DR

This paper introduces a new variety of local smooth diassociative loops that satisfy the Moufang Theorem, addressing an open problem in loop theory.

## Contribution

It presents a novel variety of non-Moufang loops that nonetheless satisfy the Moufang Theorem, expanding understanding of loop structures.

## Key findings

- Identified a variety of local smooth diassociative loops satisfying the Moufang Theorem
- Provides a construction method for such loops
- Addresses an open problem in loop theory

## Abstract

An open problem in theory of loops is to find the variety of non- Moufang loops satisfying the Moufang Theorem. In this note, we present a variety of local smooth diassociative loops with such property.