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Abstract

The quatedral loop hybridizes the structures of the eight-element quaternion and dihedral groups. These three loops share the same character table. The quatedral loop provides a natural example of a nonassociative loop with a well-behaved Frobenius-Schur indicator. The aim of the current paper is to survey the properties of the quatedral loop, and to identify its multiplication group. The identification is facilitated by considering the loop as a superloop, and its multiplication group as a supergroup. Thus, the paper provides a brief summary of these concepts, and an illustration of their application.