Loop theory

Loop theory is a mathematical framework focused on structures called loops, which are like groups but without the requirement of associativity. In a loop, you can combine elements to get another element, and each element has a unique inverse, with a neutral element (identity). This concept helps mathematicians study symmetrical patterns and algebraic systems where the associative property doesn’t hold. Loop theory has applications in geometry, physics, and coding theory, offering a way to analyze systems that are more flexible than traditional groups, allowing for the exploration of complex combinations and structures.