A Moufang loop is a type of loop that satisfies a specific identity known as the Moufang identities, which are particular algebraic properties that make it a special case of a non-associative algebraic structure. These identities ensure that certain expressions involving the loop operation are equivalent, thus providing a level of structure similar to groups. The significance of Moufang loops lies in their connection to quasigroups and loops, particularly in how they relate to the study of Latin squares and their applications in combinatorial designs.
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