Gyrogroups: Generalization of Groups

A gyrogroup is a non-associative algebraic structure, which is a natural generalization of a group, arising from the study of the parametriza- tion of the Lorentz transformation group by Abraham A. Ungar. Gyrogroups share many properties with groups and, in fact, every group may be viewed as a gyrogroup with trivial gyroautomorphisms. In this talk, we indicate strong connections between gyrogroups and classical structures such as groups, lin- ear spaces, topological spaces, and metric spaces from the algebraic point of view.