The Thomas rotation formalism underlying a nonassociative group structure for relativistic velocities (Q919106)

Physics is a major external source of mathematical theories. It is shown here that the Thomas rotation effect of special theory of relativity (STR) gives rise to a ``group'' structure for the set of relativistically admissible velocities. This group structure turns out to be noncommutative and nonassociative. The term nonassociative group is justified by two illustrative examples demonstrating that the new concept of the nonassociative group is forced on us by the study of the laws of relativistic velocities.