How is the moufang loop used?

A Moufang loop is a type of algebraic structure that generalizes groups. It is particularly useful in areas such as abstract algebra and geometry, where it can be applied to study properties of loops that exhibit some group-like behavior without necessarily being fully associative. Moufang loops are often used in the study of alternative algebras and have applications in various mathematical fields, including topology and combinatorial designs. Their properties also lend themselves to the exploration of symmetries in mathematical structures.